Yes, cats can get sick from flea shampoos, but it depend a lot on whether the shampoo contains an insecticide and if so what sort of insecticide. Cats are vigorous groomers and this grooming will be stimulated if their coat is wet or if they sense there is any foreign material on it (this can include shampoos). When they lick their coat they will ingest any chemicals applied and this may make them ill.
Firstly you should only use a shampoo that is recommended for cats. Always use it according to instructions. Watch for any signs of ill health afterwards….in particular drooling, vomiting, wobbliness or weakness. However you should consider one of the spot topical applications that are applied monthly. The better ones are not organophosphate insecticides and have a VERY high safety margin. They are available (with good advice) from your vet and can be purchased over the counter without a visit fee. An important part of flea control is cleaning up the flea breeding ground which is generally wherever your cat sleeps (cat basket, sofas, carpets, etc). It is also important to treat all dogs and cats in the household.
Now the blood in the urine is a totally different issue, very unlikely to relate to the flea shampoo. In a young cat it usually indicates a urinary tract infection, most often cystitis (bladder infection or inflammation). Occasionally there can be some vomiting. In male cats blood in the urine is particularly important because they can get blockages in the terminal urethra (the penis) that can be VERY serious. Blood in the urine is something that must be assessed by your vet. This will be an urgent visit if he is showing signs of abdominal pain, strains a lot in the litter tray or is unwell. Please do not treat this lightly. It may be as simple as an infection but a blockage can kill a cat within a few days.
Your vet will very easily determine what caused the blood in the urine and may prescribe antibiotics or diet change to rectify the problem.
I hope this has been useful information fro you Chrissy. Please contact me if you have any further questions.
Good luck, Peter