Leopard gecko shedding?

hi my leopard gecko has been trouble shedding. She has shed stuck on her toes and I've been trying to get it off with a q tip and water. I've tried putting her on warm water, warm water with olive oil and warm water with pedialyte. I've also tried she aid by zoomed She also has a patch of stuck shed on her tail and its at like the base of the tail. I'm scared to take it off because she gets startled and I don't want her tail to detach. And she has skin around her mouth and ear as well! How do I loosed the skin up?! Any tips for getting it off? Thanks :) her temps are 86-90 on warm side 77-80 on cool side she also has a moist hide in the middle and I use paper towels as substrate. Ps. She rarely has shedding issue. But she was very sick and didn't eat and had diarrhea recently but she recovered and she eats and has solid poop. XD thanks again