At this point,what you have may be a varicose vein (this is the most likely differential that comes to mind). Varicose veins
in the penis rarely involve the head.Varicose veins
are simply engorged superficial veins
that may be noted even when the penis is flaccid.
Without pain, redness, change in urinary pattern ,there seems to be no indication for further intervention. A penile ultrasound may help exclude a blood clot.