It's almost always very difficult to answer "what are my chances" because it depends on so many more things than you can write in a post.
To be clear, I'm a graduate student myself, and I'm not on an admissions committee. But I've been a student for awhile and at several schools and I've seen students do well and students that don't do so well. Given these caveats, here are some of my thoughts:
1. The majority of graduate students will be much older than you. There are certainly graduate students that are as young as you but you will be an outlier. In one of your paragraphs, you wrote something like "will my age make up for my poor GPA", and the answer, in my opinion, is No. I think your age is actually an extra obstacle to overcome, not an advantage. But see the next point.
2. Age is not going to be a direct criteria in judging applications because schools will want to avoid age discrimination. But committees are made of humans that are not 100% objective. In addition, while starting college at a young age may be impressive, I think this is only an advantage if you are very successful despite your age. Instead, to be honest, your GPA isn't very good and you don't have any research experience.
3. Doing well in this last semester will make a difference. Trends in GPAs are important too, not just overall value. However, I am wondering why you are finishing this semester instead of at the end of the academic year? If you want more time to improve your GPA, then why are you finishing "early"? (Or have you already finished 4 years of school and this is an extra semester because of your double major?)
4. Finally, from reading your profile, one huge thing that is missing is that I do not get a sense of why you want to go to grad school. What are your motivations? What interests you? Maybe you just didn't write it, but why grad school? I think having a good reason and a passion is very important for admissions and this is going to be a key factor that faculty will evaluate for when considering you! How will your own life/career/academic goals be achieved by going to grad school? You said that when you started college, you didn't know what you were doing or what you wanted to do. Don't go into grad school with the same mindset!
I'm sorry if the above was harsh but I think these are important things to consider. I've met many students that start college and/or grad school really young and while some of them do end up succeeding through college and beyond, there are others that needed more time. These students did succeed later on and they say that they did feel like they started college too early.
Anyways, you asked for what you could do to become a competitive graduate school applicant.
I think the very first thing you must do is determine why you want to go to graduate school. Please don't go to graduate school if the answer is "I don't know what else to do" or that it just seems like the logical extension of school. Ask yourself what your goals are and how graduate school can help you get there and why other things you could be doing will not get you there.
Next, as you said, you do need to find research opportunities so that you can get a feel of what graduate school and research is about. It is much easier to get these opportunities while you are a student than when you have already graduated. So, one thing you could do is to delay graduation. Is there a reason you need to graduate this semester? Can you reduce your courseload and spread it over a couple of semesters? With a reduced courseload, you can then sign up for independent study (i.e. research) courses or maybe even find a research assistantship to work on part-time. I'm writing this from the point of view of a Canadian school where doing this does not increase your costs at all, but I have heard that this can be unaffordable in the United States. So maybe this won't work.
In order to find more research opportunities, you need to "plug in" to your school and department community more and be more involved. You said that you have been passive in the past and you don't know what your professors do. Here are a few things I think you should do in order to "get connected" with the community at your school:
a. Is there is student association for physics? Join them! Spend your time between classes in the social and study spaces that the association may have. Go to social events to meet other students and postdocs and faculty. My undergrad's student association regularly held events that are meant for students and faculty to get to know one another. In my final year, I only had classes on 2 days a week but I spent 5 days a week on campus, from 9 to 5 ish, just working on my homework etc. in the student spaces.
b. Talk to your professors. I would be surprised if ALL of the professors' websites are so outdated that you can't even tell if they are doing quantum or astrophysics. But if this is the case, just look up their papers in online article databases. Read the abstracts and you can get a sense of what they work on. Then, email them and say that you are considering graduate school and you would like to talk to them about their research. If you make an effort to talk to a lot of people, you will get noticed and stand out in a good way.
c. Go to seminars! Your department probably has a weekly colloquium or seminar series where they get guest speakers (or sometimes speakers from your own school) to give lectures. Attend these seminars and you'll be exposed to more research and physics beyond the classroom. Maybe you'll find something you're really interested in. Also, you will see your professors there and pay attention to who is interested in what. You can even learn what their own interests are from the questions they ask. And there is often a coffee & cookies or something served either before or right after the seminar. Attend those. Talk to the professors, postdocs and graduate students there about the talk you just saw or the one last week etc. It's scary at first to jump into the existing community but once you start regularly attending, you'll establish yourself as part of the community just by being there.
d. Look out for other seminars in addition to the big weekly departmental one. At most schools, there are more informal seminars where students present work as well. This is a good chance to meet the graduate students. These seminars may not be as well advertised, which is why I advocate for being "present" in the department more. You will increase your chances of learning about these things as you meet more people and spend more time in the department.
Finally, if you can only be at your school for one more semester and all of this is not enough (or there isn't enough time), you might want to consider taking some time off. You are still really young, only 17! A lot of graduate students start at 22 or older, so I don't think you need to rush into graduate school right away. As I said above, I did not get a sense of purpose of why you want to be a graduate student from your post. It might sound like a cliche, but maybe some time away will help you "find yourself" and determine what your goals are. Try some new things. You can find work with your bachelors' degree (maybe in physics/science, maybe not). Once you know what you really want to do, then it would be a lot easier to set out and achieve that. It's okay to leave physics/science for now and work on something else and then try to come back as a research assistant before applying to grad school. I know a lot of current graduate students that did something like this!