Hello and thank you for your question,
I don't think your doctor will have any problem prescribing you Fiorinol #3. This medicine does contain Codeine, which is a narcotic, but if you never abused narcotic prescriptions, your doctor should have no problems giving you that medication.
Something else to consider, if you have migraines daily, is to take a medication which will prevent migraines from coming instead of taking something which will stop them while they are already there. There are several different types such as Topamax and Gabapentin. You take these medications daily to prevent migraines from happening in the first place.
I hope you find this information helpful. Please feel free to follow-up with any other questions you might have.
If you are satisfied with the answer, please do click 'Accept' button so that I may get credit for my work.
Best wishes and good luck,