Hi and welcome to Just Answer. I am a licensed veterinarian and will do my best to help you.
Thank you, XXXXX XXXXX very concerned about my cat
This is a very important medical condition of cats and you are right to be concerned. I am pleased to see that he is passing urine when he tries to urinate. Were he not able to pass urine, even in small amounts, that is an emergency and he would need to be seen immediately. It is common for them to urinate a small amount frequently, and that is not a concern. Certainly, feeling his abdomen to determine if the bladder is full and painful is a great way to determine if he re blocks again
I do this with the cat standing. Placing your hand between the rear legs with the thumb on one side of the abdomen and the fingers on the other and push upward toward the spine. Keep you thumb and fingers about 2-3 inches apart as you gently slide you hand forward towards he head. A very very full bladder will be between the size of an lemon and a medium sized orange and be located about halfway to the ribcage. Nothing else is that large, firm and painful if he is blocked.
As he improves he should lick his genitals less, pass a larger quantity of urine and urinate less often. The pain medication should also help with him straining less. Ideally he should be on a high water content diet- either canned food, or add water to the c/d and let it soak until it is the consistency of canned food (1-3 cups of water per cup of dry food). The high water content will result in more dilute urine making crystals difficult to form, and will help flush out the bladder as he will urinate more often. Dietary management is forever with these cats, though you could more to a regular canned food and not c/d after the first month.
Here is a great article on this condition: