Breaking hair is nothing to go to the doctor about... especially if it's healthy at the "roots". The thing is, once your hair is out of the follicle, it's dead. It won't heal. Different things can damage your hair... mechanical (brushing, etc), environmental (sun), chemical (hair dye etc), thermal (your flat iron.)
These various things break different bonds in your hair and damage your cuticle, the protective layer of the hair, which makes your hair more vulnerable to further damage, causing trichoptilosis and monilethrix and overall brittle, damaged hair.
Once your hair is damaged to the point of breaking, the only way to fix it is to cut it off. Use a thermal protectant before flat ironing, and you can use a high quality keratin conditioner... joico k-pak has a good rep. Also, using a moisturizer can help the hair feel softer and lessen the signs of damage... biosilk and paul mitchell's "super skinny" are slippery type products that will make your hair smoother, you can also use leave-in moisturizers with botanical oils and such.