While fasting I noticed semen coming out and I cleaned the area and then prayed and continued my fast. Should I have performed full purification (ghusl) and is my fast still valid if I didn't?

Your fasting is valid. This discharge you saw may be not a semen, because semen is affluently discharged upon reaching orgasm in which case it is obligatory to perform purifactory bath (ghusl) for the validity of prayer and fasting.