Hi Gwenan,
Welcome! I'm sorry to hear your suffering. Unfortunately triptan medications can cause rebound headaches which can also trigger migraines.
I have tried stopping medications that cause me rebound headaches cold turkey and end up in the hospital or taking a lot more medication fixing the headache. I have found the best way to is to slowly reduce the medication causing the rebound headache - though I have no medical education just lots of first hand experience.
Figure out the dosage your taking every day and then set a schedule and take them at set times like 9am and 12 pm if you're taking them 2x a day - or whatever is closest to your regular schedule and then start reducing by 1/2 or 1 tablet every 3 days to a week. As there will be pain you will want to device a pain management plan to make it manageable while you're reducing to zero. I have never weaned off triptans but have done so off Tylenol 1s and Tylenol 3s several times.
With my most recent experience I started taking 4 Tylenol 3s - 1 at 7 am, 1 at 12 pm and 2 at bedtime. Then I reduced by 1/2 tablet every 5 to 7 days. When I have had headaches I have taken Toradol, a prescription pain killer that isn't a narcotic and not known to cause rebound headaches, or Advil Liquid Gels or Robaxacet. I'm down to 2 Tylenol 3s a day now and the experience hasn't been really bad. The rebound headaches are significanly less, I have had 2 days in the last two weeks without headaches and four days this week where I didn't wake up with a headache.
If you search the internet for rebound headaches there is a lot of information out there about reducing medications causing them. There are also some good books. Just be careful because some people (docotors) will tell you to go cold turkey (stop suddenly) and if you've been taking them for a long time the shock can be devastating on your system.
Good luck! Let us know how it goes.
Nicky
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The secret of health for both mind and body is not to mourn for the past, not to worry about the future, or not to anticipate troubles, but to live in the present moment wisely and earnestly. Buddha