Has leftsided ulcerative colitis. Feel discomfort / irritation inside rectum for few hours after waking up. How to get quick relief? Any medicine?

Depends. Would use either Canasa suppositories at bedtime or Rowasa (mesalamine) enemas in addition to oral meds, but check with your managing physician first to be sure the above recommendations are valid.
Ulcerative colitis. The fastest relief can probably be obtained either with a cortisone enema or cortisone pills. You will need a doctor's prescription for these.
Topical. You may indeed need adjustment of your medication management with particular attention to adding topical therapy.