[Eternal]

If you don't like your medication, I definitely want to encourage you to talk to your doctor. There are several different medications for bipolar disorder, so if the first one you tried isn't working for you, then you can switch until you find some that work and help you.
As for your question, it is normal. In fact, it's a good thing that you feel comfortable enough to cry in front of your boyfriend. If you're afraid you are wearing him down, then I encourage you to talk to him. Tell him how you're feeling and that you are worried you are upset too often. If he respects you, he will reassure you that it's okay and he is here for you.