So IIRC prayers used to be fairly useless for sickness (lower priority than healing, and the fever always re-damaged you after prayer. Looks like that changed at some point...

Running around PC6 with sickness after eating a kobold corpse (first I've eaten in about 10 years, I'm in hospital, playing with graphics for the first time, and my attention span is awful right now). I run into a fire vortex which will definitely kill me, so I get right next to it and pray for health to give me the HP to survive...

...Lolth cures my sickness, and I die to the fireball. BAM!

On the plus side I'm glad you can pray away sickness now! I just need to retrain myself...