I would not cut your hair all off if it's not that bad. After three months you could probably use a light trim anyway. How were you keeping you hair moisturized and conditioned duing those months? That could have more to do with your breakage than having fine hair. My hair is fine and I don't have a problem with twists or braid but then I don't leave them in more than three or four days.
"More people would learn from their mistakes if they weren't so busy denying them." - Harold J. Smith.