I have stopped taking medications that were causing me rebound headaches several times and never had to go to the hospital. In fact where I live it has to be a life or death situation before they will admit you to the hospital for withdrawl from medication.
For me rebound headaches are dull headaches that sit behind my eyes and seem to last forever. My neurologist suggested taking something like Advil Liquid Gels or Aleve Gel Caps to relieve the pain. It doesn't work completely but it can mask the pain. I asked about two that won't bother my stomach because I've developed ulcers from too much pain medication use, these two are pretty good and the neurologist says aren't likely to cause rebound headaches.
I end up eventually feeling like I want to tear my hair out because it's a dull pain that just won't go away - though it does eventually. Sometimes a sleeping pill or melatonin helps so you can sleep because I find sleeping difficult. If you can tough it out you'll feel better in the long run. You'll have to decide if you're going to do it cold turkey or slowly. I would discuss that with the doctor, some medications its not safe to stop quickly. I don't know about triptans.
If you need some moral support just post a message. I'm on day 7 of a rebound headache. Monday and Tuesday were pain free in the day though the headache came back in the evening. I'm weening off pain killers slowly and I'm ready to tear my hair out. The first couple of days were really rough and I took it easy, the next couple better and next couple even better and today I had a set back and the headache was here all day.
Take it easy on yourself, avoid stress and treat yourself to things like warm relaxing baths, massages, and afternoon naps.
Good luck. I will think lots of good thoughts for you.