hi canIstay and
yes, it can get better. there are tools and resources here (im a huge fan of the communication techniques) that can help you improve your relationship; a lot of that improvement is likely to be at your initiative, and ideally (no guarantee) he will follow your lead. people with BPD are hyper in tune with (real or perceived) changes in our attitude; that might be what he was sensing.
i recall a similar pattern in my relationship, two weeks stress free, no fighting, yet it left me walking on eggshells trying to avoid triggering the next explosion.
to answer your specific questions, medication will not cure BPD though if he suffers from say, anxiety or depression, which can exacerbate BPD, it can help treat those symptoms. therapy (particularly DBT) has a great deal of promise, though there will almost certainly be ups and downs in the course of it; confronting ones inner turmoil is scary.
have you had an opportunity to read through the lessons here (you can find them directly to the right)? there are innumerable resources that apply to, and can help you better understand your situation.
can you elaborate on him pressuring you to make a commitment to your future together? is he pressing for marriage?