How old are you? Do you have a history of knee or leg injuries? If you can't run, you've got some bigger problems than playing football, and honestly I've got to wonder if you playing football is really a good idea if you're in that bad shape.
Doing sprints on grass or a track should not hurt your knees like that, and if it does, football is going to be a fucking nightmare for you.
You sound like you NEED to start dropping some weight pal. Unless you're a solid 6'5", you shouldn't weigh that much.
If you were playing for one down, well yea, you'd be right. But it's the accumulated fatigue of playing every down, over and over, and running up and down and blocking and doing this or that... football is a tough, demanding game.
In order to not be sucking wind during a game, you've got to do conditioning that you think is well above and beyond what you would need to play - and that will probably just be enough.
Look at boxers, training for 8-12 weeks, running for miles and miles and doing hours of skillwork for a bout that last just 36 minutes.
Football is much the same. For you to play 12 minute quarters (like HS football is here), you've got to do months of work. We ran every day after practice for the first four months, and we didn't stop until maybe November. By that time, you're in total playing condition and playing the games and doing the practices was enough.
But we were also practicing every day, from July to December, from 3 p.m. until the sun went down.
You, practicing only once a week, are going to have to get your conditioning in other ways, because practice will not be enough.
Have you ever played before? I'm guessin cause you're calling it "American football" that you haven't hahaha.