Is your PT any good? I've been told that some PTs are A LOT better than others - and that most of the ones that are good for athletes specialize in sports medicine. Maybe you could ask around to see if there is one other athletes like, especially flexibility sport athletes like skaters and dancers.
If it's hurting while you're sitting, I'm not certain it's your hamstring as you're not using the muscles much (although I'm not a medic).
Sitting can sometimes be a stretch. A hamstring stretch exercises my PT has given me is to sit with a very erect posture (which I usually don't have) with one leg unbent, in front of me with the heel on the floor. Then I bend forward at the waist, while maintaining the erect posture, to create the stretch.
That's only a stretch for me because I'm not very flexible. But if I understand correctly, a strain can leave you with scar tissue in the middle of the strained muscle or in the middle of sprained ligament - which effectively reduces your flexibility in that muscle or ligament. It takes a long time to work out the scar tissue, and it's possible you shouldn't do that while the scar tissue is still holding things together.
(No, I'm not suggesting you heal your strain by stretching. At least, not without proper medical advice - you can make the injury a lot worse.)
I once had a bad sprain - maybe partly hamstrings, but definitely other things too - from a backwards ski fall that forced my hips wide open (it would have been a completely gentle, much practiced fall in skates, but skis are too long for that), which my hips simply cannot do. It took 5 or 6 months of relative inactivity to heal. Like you, I initially made it substantially worse by trying to ignore it, and skated afterwards.
I'm willing to try almost anything!
It sounds like my 5 or 6 months of inactivity isn't something you are willing to try... You want a quick fix which puts you back on the ice fast. This may be out of date, but textbooks (I'm not medically trained, BTW) at least used to say any major injury takes at least 6-12 months to completely heal, including "remodeling" the new tissue, even if you do everything right, including rest and starting to ice the injury within the first 30 minutes or so, and so on. Maybe longer.
I hope you find a better answer. But maybe it will just take time, and rest, to heal.
Take care!