I'm not sure if the blood is in the urine or the bottom when the cat tries to push hard to poo. Cat has been on thyroid tablets for some time. He is 14 years old and is drinking and eating.
Either way, he should be seen by a vet right away. Constipation can turn into a serious condition as can a urinary infection, inflammation, or obstruction. His age and thyroid condition make it all the more important that he be seen.