It's hard to know off of just that information, but those sorts of pains are super common for rock climbers because muscles get unalined. If you do only one type of exercise you need to balance it. It's amazing what doing push ups, and stretching has done for pain management for me. Also talking to a physio is a good idea. Doctors are like to give you pills, but physical therapists will give you exercises that will help you manage long term.
Why is rest out of the question?
Why is rest out of the question?