What is a good way to wrap my sprained hand? Does the ACE bandage help?

No. I am not a big fan of ace wraps on the upper extremity due to improper placement and ultimately ending up looking more like a tourniquet. A real wrist brace is better and if not better soon see your doc.
Ace is a good start. A small ace that is appropriately wrapped can help. Elevation and ice helps too. Ibuprofen may help. If there is any concern, see a pcp or orthopedist.