I have a balky shoulder and my doc told me to follow her 15/15 Rule whenever my arthritis flares up again. (she's big on rules, some I even pay attention to...LOL) For every 15 minutes of activity, like coloring, or housecleaning (where I always stick to the Rule...LOL) take 15 minutes of rest. Stretch a bit (I went through PT for my shoulder so I know what you mean about knowing what to do for your neck) and go back to work. Somedays I can't work at all, my shoulder screams at me to leave it alone and I've got no choice but to oblige it. If I don't, I know I'll be sorry for days that I didn't listen to my body.
I don't like the ice routine, either, so I just do the heat routine...again 15 minutes on, 15 minutes off. My doc's 15/15 Rule, part 2. Sometimes I sit with a heating pad on my shoulder for hours. That feels soooo good.
I hope you get relief from the anti-inflammatories and pain med. Anti-inflammatories do nothing for me but kill my stomach, and I've tried them all, I think.