Hi there! I get the same thing, only it gets much colder here in Chicago. It's like my hands stiffen up. I ALWAYS wear fleece gloves. I never let my hands get to the cold air. It keeps my hands very warm, too warm sometimes, but the symptoms seem to subside. I've never seen a doctor about it, because it's not severe, but a friend that's a nurse told me to do that and it helps.
About the Advil, I wouldn't take too much. I know someone that got kidney stones from taking too much ibuprofen. If you have to take it for the pain, I'd drink lots of cranberry juice as well, just to be safe.
Hope this helps. Good luck.