Having to push hard on your door in order to get it to latch is much more common with exterior doors than interior doors. That would be due to things like weather and weather stripping. Exterior doors have more things to get through to latch than do interior doors…things that rub together to seal out the elements…like a door sweep, threshold, and the aforementioned weather stripping.
So there are a couple things you can do to try to ease the pain in your shoulder from throwing it into the door to close. You can first try to adjust the door’s strike plate so that the door doesn’t have to travel as far to latch. You would effectively be moving the strike plate away from the exterior side of the door. This might not be so easy, especially if you are only moving the plate a small amount. The screws may tend to wander back into the old holes. If this works, great…but don’t sacrifice gaps in your door weatherization so that it is easier to latch. If you can see daylight, that is a problem. You can also try to use a metal file and file away a small amount of the door strike.
You can also choose to replace the weather stripping. You might try a less dense weather strip so that it compresses easier which will allow the door to close with less effort. Additionally, check the door sweep to make sure it is lightly touching the threshold instead of dragging on it.