I have to disagree with Hissy here, something I usually hate to do. I just went through this with my cat and uti's/flutd CAN make your pet very sick - vomiting, not eating, not drinking, dehydration, etc all happen.
The reason for the vomiting, if the infection is not caught early, and believe me it progresses rapidly, the backlog of urine gets up in the kidneys. If the kidneys become infected, vomiting and dry heaves (in my cat's case it was yellow (stomach juices) and foamy) can occur.
Both times with my Siamese he was peeing normally, and then a day later not peeing at all and what little came out was bloody, vomiting, not eating, not drinking, and acting very, very sluggish. He would growl if we touched anywhere but his head. Hiss at anyone that came near. All common symptoms of urinary problems. The best thing is to go with your cat whenever he/she heads for the litter box. Monitor exactly how much he/she is drinking and excreting. If you work, place the kitty in a quiet room with a measured amount of food and water and a litter box. When you get home, check how much food and/or water is gone and also how much waste is in the litter box. That should give you a good idea if there is a urinary problem.
The first time, the vet incorrectly diagnosed constipation over the phone and told us to feed our cat a tsp of Vaseline. By the next day, he was worse so we brought him in without calling. Ask for blood work and x-rays. In our cat's case the toxins in his blood were at 298 whatevers instead of 0 where they should be.