I am 13 weeks pregnt and having some discomfort in lower abdomen plus difficulty when trying to pee. I had a UTI at week 5. Could this be a UTI again?

It could be. You certainly could have another UTI with those symptoms. Even if it isn't, those symptoms warrant an evaluation. You should check in with your ob/gyn or midwife without delay.
Yes. Pregnancy can make some women more prone to bladder infections. See your dr for a urinalysis, & antibiotics if necessary.
Yes. Although it may be symptoms of pregnancy (your first?) it may well be a uti. You need urinalyses and a culture to determine this. Are there any other symptoms? Pain, burning, frequency, urgency, etc? You should see your ob.