That is a Blue Head Wrasse, (Thalassoma bifasciatum) looks to be a male. These are collected in southern Florida and throughout the Caribbean.
I would feed mostly meaty foods right now. Including squid in the diet can help fatten him back up but keep the diet varied.
The red spot is likely an abrasion, possibly from trying to bury itself in the substrate or perhaps got pinched in the rocks. If your substrate is coarse like crushed coral or dolomite, this is pretty common.
If this were my fish I would feed it heavily and soak it's food in Selcon & Marine Vitachem. I would keep the aquarium extra clean (water changes and filter cleaning) and use ozone injection or a fresh & properly sized uv to reduce organisms that will affect that open sore. Ozone is the better choice if it is an option. If your substrate is coarse, replace it or move the wrasse to an aquarium that has a softer substrate. (coarse substrate can harm the fishes body when they try to bury themselves.) Also, vacuum your sustrate to decrease the population of nuciance organisms and debris.
Fish are somewhat like us in that if we (and they) are properly nourished, well rested and in a clean, stress free environment, the immune system often can repair or cure what is wrong. So everything you can do to strengthen this fish and improve it's environment, the higher the likelihood it will heal. If you see that the sore gets worse, then putting the fish in a quarantine system and treating with a broad spectrum antibiotic may be needed.
Hope this helps and good luck,
Joel