I agree with the salsa idea. This worked for me too. Before I started a couple of months ago, I thought dancing with a partner was just too intimate for me and made me very nervous. I was affectionate, but being so close to someone for more than a couple of seconds (for a hug) didn't sit well.
The other dances related to salsa will help with this too (Bachata, Merengue,etc most likely you'll dance them too) because sometimes you dance them even closer. You can even have a very sexy dance with someone's spouse and it doesn't mean anything. After the song's over you look for a new partner.
It's worth learning.