Can I go out that day? Will I be red and or swollen?

You definitely can go out immediately after your permanent make up procedure. I usually tell my clients that they get as a red or swollen as they do when they get waxing for eyebrows, eyeliner can get a bit swollen because that tissue is very delicate and the lips can get a bit swollen as well. Most swelling goes down within 24 hours of the procedure.