I have had this same issue in the past, for me pushups were just extremely uncomfortable and I was never able to hit my strength limit before I had to stop.
First of all, using a punching bag for some boxing routines would be extremely beneficial for certain areas of your chest (serratus, lower outer, and upper outer chest). Most boxers rely on a strong chest for punching power so beating up a bag at high intensity for 10-15 could really only do good.
A couple of exercises I have done in Calisthenics over the past few years are:
- Put a bar over two chairs and lay on the ground, pull your chest as close as you can to the bar. Essentially, this is like an inverted bench press. Paused reps are good on this one, increasing the time under tension.
- Chest dips. They are the best done with the proper equipment, but chairs or something of the sorts will do just fine. The key with chest dips is using the right form, otherwise you will be strengthening your shoulders/triceps rather than your chest. You can either google the form or just feel it out on your own. Everyone has a different body, whatever way you feel is putting significant tension on your chest, that is the one to do.
- Resistance bands are great if you have. And if you don't, a great set on Amazon is like 30 dollars. This will allow you to do chest flys and other variants, which may be the most beneficial exercise among the three I mentioned.