What workouts should I do to be able to throw a football farther?

Mostly calf raises.

get bigger hands

Like over them mountains farther?

Tricep Dips, Squats, Shoulder Press. Plus continue to workout your core.

For a serious answer, you gotta gain more flexibility. This is the best stretch I've done. It makes your arm feel good immediately and you'll be able to throw a little further just from the initial stretch:

Push down on your hand and hold for 30 seconds and do it a couple of times:




The second thing is just throw long bombs all the time. Baseball players throw long toss. This is coming from a baseball perspective but I'm assuming it works the same way for throwing a football.



One more thing to test how flexible your shoulder is... go lay on a table or your bed or something and let your arm hang off in an "L" shape like this, just resting. I bet your arm isn't past parallel with the table. With pitchers and quarterback's, their arm goes way past parallel while resting like this:

Buy a smaller ball

/thread

Cock pushups.

You only need one

I've been throwing footballs for 30+ years and always had a decent arm but nothing special. Just a couple of months ago, my buddy had a slightly deflated football and I felt like I had much better arm strength than ever before.

Since you mentioned that it 'hurt to catch', I wondered if it was over-inflated which is more difficult to get distance but might hurt more to catch. Try the Tom Brady solution of slightly under inflating them.

Kegal exercises