I had catheter ablation for SVT and atrial flutter yesterday. Should I feel a different heartbeat if I'm cured?

Yes. If you were constantly in an abnormal rhythm and the ablation was successful, you should feel different. However, if the rhythm was intermittent it may be more difficult to discern a difference.
Not necessarily. Some individuals do not have symptoms or feel their rhythm disturbance. Others that do have palpitations or other symptoms often feel immediately better.