I'm not aware of any such exam, and I think that you are probably underestimating the level of difficulty in upper-division physics courses. To self teach up through a Bachelor's degree level would be quite an astounding feat.
In my department, physics majors need to take (at a bare minimum) the Intro Sequence, Waves and Optics, Modern Physics, Mechanics II, E&M II, Quantum I, II and III, Statistical Mechanics, and two advanced Labs. Math requirements are Diff EQ, Advanced Calc II, and 3 additional upper-division math courses.
The two solutions, if you really want a physics degree, are:
1) Switch into physics, or double major. I imagine a double major would take quite some time to complete, so that may not be feasible for you.
2) I'm actually a Computational Physics major. If your school has multiple physics degree plans, they might have something similar that might interest you. The requirements for me are basically the above listed Physics courses, minus one of the labs and Quantum III, but plus a Computational Physics course and an Electronic Techniques course. I have to take 4 core computation/programming classes. The upper-division math requirement is changed to 2 upper-division "Math or Scientific Computation" courses. Since your only a 2nd year student, you could transfer into a program like this (at your school or maybe even another) and likely still graduate on time or close to it.
Edit: I should have mentioned that I believe that anyone can take the Physics GRE subject test. Unless you wanted to apply to grad school though, I am not sure it would benefit you substantially, other than serving as proof of your knowledge. See:http://www.ets.org/gre/subject/about/content/physics