Brief Answer:
Read below.

Detailed Answer:
I read your question carefully and I understand your concern.

There are two types of treatment for migraine, treatment for the acute attack and preventive treatment which aims to reduce the frequency of attacks in the long term not alleviate the acute pain.
Treatment for the attacks may be nsaid like Ibuprofen, antiemetics or triptans like Imitrex (sumatriptan). Triptans are the most effective drug for acute attacks so I wouldn't change it.

What must be done in your case is pay attention to prevention. It is unclear whether you're taking anything for that purpose now, you have in the past, drugs like elavil (amitriptyline) and propranolol are aimed at that and if they were effective may be resumed. Now as for the effect on central nervous system you must understand that since they all are used for a nervous system condition they all have some potential for side effects on nervous system (not necessarily though). So that can't be taken completely out of the picture. If Elavil or propranolol weren't effective or had many side effects the remaining first choice option remain anticonvulsant like topiramate or valproic acid, but as I said they might affect your central nervous system. Another choice but a second choice, less likely to be effective, one are antihypertensives. I have had great experiences with flunnarizine, a calcium channel blocker in my patients, but I am not sure it's present in the US where you live. Other antihypertensives to be considered are verapamil or candesartan.

A last option recommended when at least three drugs fail is botulinum toxin injections which would perhaps suit your concern of not being affected in your study.

I remain at your disposal for further questions.

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