髮型師整親我個頭,有沒有可能有賠償!?

This is a matter of Tort Law.

Generally speaking, the hairdresser has a general duty of care to his customers under the contractual relationship of providing hairdressing service.

If you are injured during the course of his service, he may be liable for damages to you. Furthermore, the salon (company) employing him may also be liable to you under vicarious liability.

As to a future consequence (causing a permenant hair loss), you will need to prove both legal causation and factual causation of the permenant hair loss by his wrongful doing.

Frankly... if you are getting hair loss now, you will have a better case than your hair loss starts 3 or 4 years down the road. A good solicitor will help you to prove this case.

I dont see a need to write to the salon to reserve any right for future legal action, as this duty of care is well established in a contractual relationship of service. But of course, if you just want to alert them with their wrongdoing, a letter from you will be helpful.