Katie, 15 pound DBs for chest press is a very respectable weight, so
on building up your strength! Chest and shoulders are my weakest body parts, too.
I think it's OK to swap your DB chest press for pushups because they're going to be working the same muscles with both exercises. In fact, pushups are a more challenging exercise because they require the use of stabilizing muscles in your core and legs that aren't used in the chest press.
Or you could alternate the two exercises for each workout -- chest press one time, pushups the next, then back to chest press?