I have been where you are with narcotics. I have tried every medication known as a preventative or abortive for my migraines. Narcotics (only some work for me) have been the only type of drug that catches or releaves my pain. People that take narcotics for pain become dependant, which only means you body chemistry gets used to having the medication in your system. If you take it as instructed, it will relieve your pain, but you won't feel "high". If you stop taking them cold turkey, your body will let you know about it. It is far better to taper off them, and limit the stress on our body.
Some people become addicted to narcotics because they take far more than prescribed for their condition, because a higher dose will give them a "high". These people will seek out mulitple doctors for prescriptions and will use different pharmacies to fill the prescriptions. They have to continuously increase the amount they take to keep the same level of "high". They will also buy them off the streets if they can't find another option. Their withdrawal will be much worse, because a lot of them end up having to stop cold turkey.
Although narcotics will help your migraines, if you take them, triptans, or any OTC pain rememdy more than twice a week, then you will start causing yourself rebound headaches, and pretty soon you end up with a headache every day. This behavior prevents the preventative medication from doing its job.
If you are concerned with getting "mental" problems, you should consult with a psychiatrist. You may need some coctail of anti-depressants and anti-anxiety medication, which most migrainuers take. This can also help with the frequency of migraines, if stress influences how often you get your migraines. As far as early dementia and permanent brain changes, I have never of such a thing, and I've been dealing with migraines for 33 years. Migraines are often caused by a chemical imbalance in the brain, which is why we take medication to restore the balance. I really don't thing you have to worry about losing your mind. I've never heard of that, EVER!!!
There is no shame in taking narcotics if that's what it takes to do the job. Consider yourself lucky that you have a provider willing to continue prescribing them. Mine cut me off cold turkey, after I had to see another doctor in her group, who threw up a red flag about prescribing narcotics to me for too long. Most doctors in this area are very wary of prescribing narcotics.
My mother always makes comments about what would happen if I just stayed at home and stuck out a migraine. She suggests that that situation is going to happen, because the doctors are someday going to refuse to treat me. She had no comprehention about that level of pain. It would kill me. I know because I've tried before and just can't do it. I'd end up tidying up my house and slitting my wrist to relieve the pressure. Mind you, I'm not suicidal, my mind justs interprets it as opening a pressure valve. I will never let myself get to that point. Even as crappy as it is living with the constant migraines, it's not worth dying over.
Best wishes and let us know how you are doing,