Yeah, I recommend shaving her fur. Try not to cut it too short, to avoid shaving her skin (hurts thinking about it). I’m not too good with medications and stuff, but I do know a little about how to help.
Have you tried using a cat flea comb? Get the ones with dual sides, since they work really well. You could even try human lice combs, for extra support. When using the metal combs, be careful not to brush too close to her skin, since it could pinch and hurt her. I don’t really know much about Dawn, but you should probably dilute it before you dip the comb in.
Make sure to vacuum her room and even the blankets she uses, maybe even vacuum the entire house or at least places she travels, since they could spread. Vacuum especially after you comb or shave her out, and don’t let any fleas escape! Kill the fleas as hard as you can. This is your time to let all your anger out. Don’t leave a single one alive. Let us know how it turns out, dear!
Wish you the best! xoxo