Sweat got stuck under dark burnt skin where I had a blister. Should I do something about it? Will effect healing my burnt wound?

NO. I am not sure how sweat stuck under burnt skin but is will not matter. Leave it alone and not puncture the blister. It may dry from below or rupture on its own. As long as not red it should do ok. You will want to clean this daily and prevention of any dirt in the wound. Tincture of time. Ie be patient.
NO NO. Sweat is not harmful in a wound. Keep it lubricated with vaseline or Aquaphor. Water is good for it. Avoid peroxide, alcohol, iodine, or any other antiseptics. Avoid bacitracin, neosporin, triple antibiotic, or any other antibiotics.