Well, quite frankly…you earned a C+. So you can’t tell your teacher you deserve a C+…because that’s not what you earned.
One of the most valuable lessons you can learn in college is about balance, and learning to juggle competing priorities. You learned that lesson in perhaps a harder way - by failing some exams when you realized you were overloaded with STEM classes and ROTC. Having overburdened yourself, however, is unfortunately not a compelling reason for a professor to raise your grade.
So no, I wouldn’t ask for a bump or tell your professor that you deserve a better grade. Frankly, personally I wouldn’t do anything. But if you really want to do something, you can approach the professor for advice on how to perform better in future physics classes.
I would say generally, professors hate it when you ask for extra credit. The prevailing attitude I’ve seen (and had myself, when I was teaching undergrads) was - why should I give you extra credit when you didn’t even perform well on the first material you were given? You (not you, OP, but the general you) had the same opportunity to perform well as everyone else in the class, and you didn’t take it then. Why should I extend you another chance? Often the students who asked for extra credit were students who didn’t even do the originally assigned work.
Even offering it to everyone is not fair, because extra credit inevitably helps out the students who are doing poorly much more than the students who are doing well. If you have an A in the class, the extra credit is not going to bump you up to…a higher A? It may not be worth it to do some extra credit in late December when you’re preparing to go home. It’s mostly the C and D students (and maybe a couple hypercompetitive borderline B/A students) who will take the extra credit.
And given that at this time of year grading is already down to the wire, a professor might resent being expected to do more grading right before the holidays.
So I wouldn’t ask for extra credit. Almost every professor I know is more annoyed by this request than anything else.