You've been given some great advice so far. With your bout with UC being only one month to colostomy, everything going so fast, it is hard to get your head around all the changes. Its hard to know what is a new "normal" and what just isn't right. I had that issue too, only mine was a few weeks longer than yours between UC diagnosis and surgery. It is a huge change, that I wasn't ready for. My former GI said "I'd be cured" with the surgery. Never warned me about what a j pouch is like. I really understand how you feel.
I would try to slowly add some soluble fiber to your diet. This will not only help with thickening (less bowel movements), but also with transit which should help prevent straining. Hopefully, it will help your gut feel like it emptying completely without always feeling something in the anal canal. Also if you haven't already talked to your GI, I'd do that and have him/her check for pouchitis or inflammation. He/she might recommend something you can do for the constant feeling in the anal canal as well.
Once again, your pouch is fairly new. It took me a long time to get to my new "normal". I found a new GI who helped me with medicine to get to that place. Don't give up trying to find some answers.
Thinking of you!