What is the correct treatment for such cases, and will this jinn remain with the girl after I marry her, given that she drank sorcery and experiences vomiting and lower back pain on specific days?

We do not know whether what the woman is experiencing will continue or not, as this is an unseen matter. If she is religious and of good character, there is no harm in marrying her, for sickness and healing are in the hands of Allah. We advise you to perform Istikhara regarding marrying her if she is religious and of good character, and then do what your heart feels at ease with.