Ice water bath for recovery?

Is just "muscle soreness" (which is not actually muscle soreness, its inflammation in the connective tissue), it's fine to workout with it, and it will probably make you feel better.

Stretching helps as well.

I do ice baths quite frequently during my peak training cycles (after long runs, long rides, etc). Research has shown that the water does not need to be ice cold but around 50 degrees. I usually just fill the bath tub with cold water and "jump" in. I add actual ice about 25% of the time as it just melts within seconds anyhow. I typically wear a pair of compression shorts and a sweatshirt just to keep things a bit warmer. Some people have found that sitting in the tub and filling it with cold water is easier than just jumping in but I prefer my pain all at once. It is super cold for about 30 sec and then everything just goes numb.

You can try an ice bath to help with any inflammation. It does work wonders. But without more info on the type of pain it is hard to give further advice. It is is actual pain and not post workout soreness, I wouldn't push through it. Pain means inflammation and possible injury. Soreness just means youre doing it right. Another option that would might help (for both pain and soreness) is some myofascia massage - take a tennis ball and roll it on your glute. You can just place the ball on the floor and roll around on it. If you get to a super sensitive section, sort of stop on that area for 20-30 sec breathing through the pain. You could also foam roll if you have a roller but a tennis ball works a bit better.