Probably a split. Doubt you actually have a "cut". Most likely a split in a somewhat tight foreskin (phimosis) and a result of retraction, either manually to urinate, with masturbation or sexual intercourse. Worth using some antibiotic ointment such as bacitracin, neomycin etc. Need to see dr. If swelling extends down penis which could signify cellulitis needing antibiotics. See urologist if you have phimosis.
See doc. Sounds like you need that looked at please.
Keep it clean. Keep the area as clean as possible, disinfect with an alcohol swab, and put antimicrobial ointment if desired. Absolutely no sex until its healed. If the swelling continues or you develop fever, difficulty urinating, or worsening pain, go to your doctor to have it examined and a prescription for antibiotics.