I have this same problem. It's not very visible, but if you look closely, my left side has more facial hair than the right. You don't necessarily have to trim the side with more hair. Remember that if you are still young, and you have been growing for a short period, your beard is still maturing, so you have to give it a little time to see what your beard will actually look like. Just for curiosity, how old are you? How long have you been growing your beard?

A tip that i give you that others more experienced here gave me is to look for strong points in your beards and not to focus on the weak ones.
Please, share your pictures.

Stay strong, don't shave and keep growing.