A couple of things:
First of all, if you want a PhD in physics, your goal shouldn’t just be to get in anywhere. It should absolutely be a funded PhD program that is well-reputed in your field and serves your career goals. Most good PhD programs in physics provide full funding anyway, but more importantly, a PhD that doesn’t get you where you want to go is wasted time and effort. And you shouldn’t pay for a PhD - the value proposition is not good, especially if you want to be an academic/professor.
Second of all, with a GPA at a 2.3, your odds of getting into any PhD program (funded or not) are slim to nil. Your chances of getting into an MS program are pretty low, too. Yes, graduate programs do care about grades - quite a bit. It’s one of the more important evaluations they make, since they need to know that you have the foundation to succeed in graduate level academic work. While most programs probably look for a 3.5+, an otherwise outstanding student in the 3.2-3.4 range could definitely be admitted.
I’m going to be frank, not because I want to be mean, but because I want you to be prepared. Graduate programs - and academia in general - doesn’t care about the hard work you put in. What they care about are the results that come from what you do. Your undergrad transcript is only the first of many places that will be true - that will be true in passing your graduate courses, in passing comprehensive exams, and in finding results for your research work in graduate school as well as the quality and output of your dissertation. It’ll be true in your postdoc and it’ll be true in your research job. Your university won’t care if you worked really hard and spent countless hours writing that grant if you get no money. They won’t care that you labored over that paper and polished it hard if you never publish it.
To that end, graduate admissions are less interested in whether you worked really hard and more interested in the outcome (your grades). It’s also the only concrete thing they have to judge you on. Your assessment that you worked really hard is your word only.
Discussing the therapy and health issues will only help if you can point to a good outcome from it - an upward trend, for example. It sounds as if you continued to have issues with not-great performance after you got better. Unfortunately, the increase in your knowledge and skill is not reflected in your grades. That makes discussing the therapy and illness a difficult sell - you have to improve afterwards in order to discuss hardships that affected your performance (because that makes it clear that it was the hardship and not your personal potential that affected your performance).
And, to be honest…you will always be competing with people who may have had interest in science fields far longer than you (although also to be frank, I am sure that not 100% of your peers knew they wanted to study science since grade school. Some of them probably switched later, even in college. Something like 25% of science majors didn’t intend to be science majors when they entered college). You can’t let that deter you from your goal.
So, of course, the question is what do you do about it? It’s not that you can’t ever get into a good PhD program - it’s just that getting in is going to take more time and effort since you have to rebound from the mediocre undergrad performance. Here are some suggestions:
-You say that you do well in assignments but poorly on tests, and that your test anxiety or something overwhelms you. Have you ever been tested for a learning disability? If not, I might visit the office of disability services on your campus and ask for testing. It can’t hurt, and if it does turn out that you have an LD that affects your ability to test well, there are accommodations you can get - like extended time to complete exams. Do that soon, because it may also affect your later graduate work.
-You say that you are getting research experience. That is excellent. Continue to do that as long as you are in school. Then, after college, you’re going to want to continue to get that research experience. The best way is to seek out some kind of paid position that will give you more physics research experience. In my field recent graduates are often hired as lab managers; I don’t know if physics does that, but any kind of post-baccalaureate research experience you can get the better. Even if you have to volunteer part-time while you work at something else. The point here is that if your undergrad GPA is low, everything else on your application needs to be outstanding. You need to give the admissions committee a reason to disregard your GPA and take a chance on you. This phase will probably take at least 2-3 years.
-While you are in this post-college period gaining more research experience, you can also take graduate-level physics classes as a non-degree student at a local university. You have to do well in these classes - get As, and draw close to the professors. If you can take 3-4 graduate-level classes in this manner and get As and glowing recommendations from professors during this phase, you can provide hardcore evidence that you are capable of succeeding academically at the graduate level.
After you acquire these pieces, then you can probably try to apply to some MS programs in physics (some funded, some not) and a few PhD programs that are really appealing to you. You probably still won’t get direct admission into a PhD program; you’ll probably need to do an MS first, but it really depends on what you do next and surprising things happen sometimes.
Also, caveat: I’m not in your field. But @xraymancs is, so hopefully he’ll come weigh in on whether my advice is totally off-base and give you more field-specific tips on what to do 