I'm not in the USA, so any recommendations for doctors etc won't help you, but I have had 2 lots of sclerotherapy on my right cheek. They gave me a general anesthetic, because they do a very detailed scan at the same time to locate areas to inject. The first time they kept me in overnight, but that was because I was still classed as a child then, the second time I was out the same day. It is VERY swolen afterwards, and generally there is some blistering, but both die down after about a week. Both times the results have been VERY good!
Good luck, let me know if you have more questions