You could give her a mist bath to help clean the feathers, but if she doesn't like it you might be better off just leaving them sticky. She's sick and under a lot of stress already and doesn't need more. An alternative would be to dab at it gently with a damp washcloth next time you have to restrain her for meds.
She will probably put up less of a fight once she figures out that you're just doing something mildly unpleasant, not trying to kill her. You will also become more skilled at restraining her and delivering the meds, so it will take less time.
It's fine to hold her by the cheeks or the jawline, just don't do it so tightly that it's likely to cause bruises. It's OK to feel her heartbeat as long as she's able to move her chest up and down to breathe. Birds don't have a diaphragm like humans do, and if they have to move the chest up and down to breathe.
A good way to hold her is with her back against your palm and her head between your thumb and forefinger. This makes it easier to control the head and the wings without constraining the chest. Letting her grip your fingers with her feet is a good way to reduce the kicking and squirming.
This thread has some good information on restraining a bird:
http://www.happybirdy.com/mainforum_hap ... php?t=4791