Most importantly, make sure you are syringe feeding either critical care or mushed pellets.
Also that you are weighing her daily so you can be sure you are syringe feeding her enough to keep her weight stable each day.
If she isn’t eating any (or some but not enough) hay then it’s essential you are feeding her every two hours and aiming for a minimum of 60ml per day. The amount you need to feed is dependent on what each daily weight check tells you.
All About Syringe Feeding and Medicating Guinea Pigs with Videos and Pictures
I’m not sure why this would be causing her hair to fall out. Perhaps there is something else going on medically which the vet needs to check