Hello,
From the symptoms it looks like Superficial thrombophlebitis of the penis (an uncommon disease known as Mondor's disease). 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 is via ultrasound which shows blockage of the vessels. Treatment is with anti-inflammatory drugs (i.e. aspirin or ibuprofen) and most resolve within 4-6 weeks. If it persists, then surgery may be necessary. I think you should consult a urologist.
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.
also ive used ice and i have been taking ibuprofen since this happend!