The two subjects are totally different and it's unlikely that you could catch up on entire term's work. The most likely scenario is therefore that you would have to start your new course from the first year, next September. You would have enough Student Finance entitlement left to do that.
As for whether you should stay where you are until the end of the current year, that depends on your circumstances. If you're in uni accommodation, you have probably signed a contract up to the end of the year.Some will let you out of the contract if you can find another student to take over. However if you can't, or your contract doesn't allow it, then you will be liable to pay rent to the end of the academic year even if you don't live there (and you won't be permitted to stay on if you're no longer a student). Your Student Finance will stop as soon as you leave, meaning that you would have to pay any future rent from your own pocket. You would also be expected to pay back your SF Maintenance Grant (if you had one) immediately.