A challenging time this must be. Try to remember that recovery is somewhat of a roller coaster emotional ride. Most Alcoholics are deeply rooted in their own feelings. Some have had difficult pasts, myself included. But one thing for sure, you must first protect your feelings from such a relationship, if it means to let the person go, then you must follow your heart. Some have accomplished recovery on SR, some with the help of AA, rational recovery. But you have to follow your heart, if you believe your boyfriend is not willing to try, let him go.
Good luck and all the best