Hello, You are experiencing cold sensation on the penis & also have rash. Rash can be fungal infection, apply antifungal topical cream (Clotrimazole) on it. You can also take a course of oral anti-fungal (Fluconazole). You have not mentioned if you are circumcised? Make sure you pull back your foreskin daily to wash with mild soap (like dove) and water. Take care of your hygiene else the urine there can irritate the penile skin. Stay away from addictions. Stop taking alcohol, caffeine, avoid smoking or vaping. These can also cause irritants to be in your urine that can cause discomfort in the urine. Vaping causes chemicals which can get into your urine which can irritate the urethra and penis. The penis is very sensitive place. Anxiety can cause decrease blood flow to the penis and shrinkage of the penis and cold sensation. Avoid vaping if at all you do. Get clinically examined by a Urologist, get required urinalysis (R/E and C/S), STD tests done to stay on the safer side. If tests come positive, you will be treated accordingly with antibiotics / antivirals. You can also consult a neurologist. Take care. Hope I have answered your question. Let me know if I can assist you further. Regards, Dr. Nupur K., General & Family Physician