You could have cuffitis as well (or pouchits and cuffitis as they can occur at the same time), which would be a more likely explanation for bleeding. You can still have UC flares after surgery. These are usually in the form of cuffitis, which is literally UC in the area of the rectal cuff that is retained after surgery. The likelihood of developing cuffitis may depend on the amount of cuff that is retained or the severity of your UC prior to surgery. But even though the affected area is relatively small, cuffitis symptoms can be severe and be very similar to a pre-surgery UC flare, including diarrhea, bleeding, increased frequency and urgency, pain, etc. The general treatment is suppositories such as Canasa, or with Cortifoam or Entocort enema. Very severe cases may be treated with oral prednisone.
If you have pouchitis simultaneously, you'd have to treat both conditions.