You may not have an anxiety disorder as such, but you're definitely having some issues with anxiety and this is enough to seek advice from your GP. Anxiety generally arises in life as a result of stress and so whilst you're anxiety is focused on the health of your hair, there's possibly something else lurking underneath that which is causing the stress. If you were to speak to your GP, they might suggest some anti-anxiety medication or encourage you to seek some counseling so as to find the root cause of the problem. Anxiety may have manifested itself in something that is fairly easy to worry about - i.e. the health of your hair - because what you're truly worried about feels too big for you to handle right now. With a little bit of extra support perhaps you can find out what's really on your mind and deal with your anxiety once and for all.
If you're really concerned about your hair, you could try taking vitamins that will keep it healthy. Have you ever heard of
Perfectil (see here)? They are fairly expensive but they do really work so if there is a genuine issue with a lack of nutrients then it should help.