When performing a push-up, people often set up with their hand position high and wide. As they drop their chest down, their elbows go wide laterally. If you took a snapshot of them above (as in an ariel view), their set up would look a lot like the letter T. This position is easier but it puts a lot of strain on the shoulder joint and doesn't target the chest and tricep muscles effectively.
No matter what type of push-up you're performing, always set up in an "arrow formation." Basically, from an aerial view the push-up position should look like an arrow with elbows pointed back (not to the side). This position is less taxing on your shoulder joint and leads to more activation of the pec and triceps. You may find that this position is more challenging and you have to perform it on your knees. That's okay! Your push-up form is the integrity of the exercise. Do not compromise your form for anything! Practice a modified push-up on your knees and work your way up to a full push-up. Pursue your better!