28. Can a muscle strain or pinched nerve cause pain for months? Took a break from my fitness routine for a month and still feel it in chest/arm/back

Yes. When exercising did you feel a 'tear or pull' sensation? Is it chest or arm? Perhaps just persistent inflammation of a muscle/ligamentous structure, or nerve. Is it tender to touch? that would indicate a musculoskeletal structure, as opposed to in internal chest structure. Try stretching exercise, and Ibuprofen/naproxen OTC. If severe, or exertional, or associated w/ shortness of breath, see a Dr.
Yes. A muscle strain, or pull can take months to heal. A tendon injury can take longer than a broken bone. A pinched nerve may not heal on its own. If the nerve compression is not relieved, it can continue forever. Further tests, X-rays, MRI, may be helpful for a nerve problem.