Can you have side effects from increasing Effexor?

This depends on the dosage you were taking, how long you were taking it, and how much of an effect it had on you. Typically, with meds of this kind, if you decide to stop taking them, backing off should be done under a doctor's care. Just stopping all at once is dangerous, and can lead to some pretty dramatic mood swings in some people. The typical route is to slowly reduce dosage and monitor for trouble as you go. The side effects of a sudden stop in this med (or even a gradual one) may possibly include mood changes, promiscuity, death ideation, suicidal ideation, depression, euphoria, anxiety, etc.