The biggest problem you're facing is not knowing for sure whether it's a sprain or a fracture or even a break. You've got to keep in mind that a cat will not act like a person might act if they break, fracture or even sprain their leg. I've seen many cats with some pretty serious injuries that are barely acting differently at all.
I'd like you to have your little one seen tomorrow for an X-ray or at the very least a hands on exam by a vet who knows what to look for and feel for, ok?
Until then, apply a cold compress to the area. Not ice cubes, but perhaps a bag of frozen peas or a cold ice pack (not frozen as it may cause more pain and even frostbite to the skin).
As you're already doing, keep him calm and as inactive as possible. Make sure his food/water is nearby, as well as his litterbox.
You'll need to watch him carefully since depending on the injury he might have some internal bleeding happening. If he becomes lethargic or his gums become pale, if his breathing is labored or you notice anything at all that your instincts indicate is just wrong - get him to an urgent care clinic tonight.
Urgent care vets are often regular vets who have 24/7 hours.
Just in case you need some help, the list below should get you started. If you don't need this list, keep it in mind for your friends or anyone who might. I want to thank a very caring expert (Terri) for sharing
American Animal Hospital Association
" Veterinary care for sick or injured pets if they have been abandoned or if their owner is experiencing financial hardship."
Angels 4 Animals
"Services range from financial aid to complete treatment
to those pets and pet owners in need."
A credit card company for health care, including veterinary care.
God's Creatures Ministry
"This fund helps pay for veterinarian bills for those who need help."
For the elderly, the disabled, the working poor."
Feline Veterinary Emergency Assistance (FVEAP)
"Seniors, people with disabilities, people who have lost their job, people who rescue a cat or kitten."
Also, don't forget to call your local Humane Society to find out what they might have in place, including clinics or discounts at certain vets.
Call your local Pet Smart and Pet Co to find out the names of rescue groups often working through them - they will have names of vets or other options you may be able to use.