N.P.
Hi there! I had a similar problem during my pregnancy with pain especially along the top of my glutes that made it really painful to walk. It was tight muscles, and also was causing some nerve pain. Though, it wasn't sciatica in my case - if you have sciatica you would expect pain extending down you leg.
In my case, it was a chiropractor that helped. I hadn't previously seen a chiro, so it may not be the answer in your case! It actually got worse for the first couple weeks, then got better. After a couple months, she advised me to do massage therapy instead because the structural issues were resolved. When it was really bad, I had to stop going for walks for a couple of weeks, because it seemed to make it worse, at my chiro's advice.
The other thing that worked well was icing it - I would just sit against an icepack. It actually helped both the muscle and nerve pain. I'm assuming it's because it reduced the muscle swelling and the nerve pain was caused by the muscle irritating the nerve.
Hope that helps a little - I know how frustrating it is!
N.