Cat peeing painfully. Will he get better on his own after vet care?

Poor Kitty Kins. It sounds like he has either lower urinary tract disease, stones or has a partial urinary blockage. None of these conditions improve on their own, but instead require some level of treatment or management.
So the treatment they gave him so far is basically they drained his bladder and treated him for an underlying urinary tract infection. However if he is developing a blockage he will need to be catheterized and treated with medications to help keep his urinary sphincter relaxed. You are doing the right thing by feeding him canned food, as this will increase his water intake and help promote a healthy bladder.
However if he does become completely blocked (blocked Tom), he will need emergency procedures to free up the blockage and empty his bladder, as they mentioned already. I totally understand not being able to do the procedure the first time around due to cost. Unfortunately this cost is pretty standard for these types of things.

Here is more information on urinary blockages in neutered male cats so that you can know what to look out for.
http://www.veterinarypartner.com/Content.plx?P=A&S=0&C=0&A=1111

And here are some financial resources that may be able to assist you in the near future:
carecredit.com
redrover.org

If he stops peeing at any moment, then he needs to go back to the vet for emergency procedures to unblock him and provide him immediate relieve. Being blocked for a period of just 6-12 hrs can prove detrimental to your pet. I hope you get things sorted out soon. Take care.