Trust Issues: Does running away make me a coward?

My boyfriend has trust issues with me-I have not giving him any reason what so ever to think that I would cheat or stray, He has even accused me of sleeping with guys while I am out spending time with my brother...He did ask a girl out while we were together and dumped me to see her. Things didn't work out for those two and I decided to forgive him and give him a second chance. But now he keeps having "trust issues" with me and starts picking fights...Is it me (being crazy) or is this really an unhealthy relationship-I have never dealt with this before and because I have falling in love with him (Im not sure if this is a good or bad thing) I dont really know what to do? Do I really stick around, pray for the best, and continue to deal with this? I don't want to feel like a coward and run away from problems, but I dont want to end up a fool either...Please Help me with some words of wisdom!