Hello,
This can be due to varicose veins or Mondor’s disease. It is superficial thrombophlebitis of the penis. This is an inflammatory reaction to a clot within the vein. This subsequently causes blockages and dilation of the vein. It is typically painless, but can be painful. In studies, patients were noted to have thrombophlebitis after a prolonged sexual act with or without intercourse. It was described as cord-like thickening of the superficial penile veins.
Diagnosis can be confirmed by ultrasound. It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.