I am 19 years old, 5'6" and 145 lbs. I have 34DDD breasts. Is there any way to naturally make them smaller?

No... you can, however, purchase bras that are designed to minimize your breast size. Be sure, as well, to make sure you have a proper fit to be more comfortable. Clothing choices can also be made to help minimize their appearance.

Some women will lose some size when they experience some weight loss, but that is very individual.

Sorry no, you are what you are, as noted be sure you are using proper bras

I already know how to hide them pretty well, I just wanted to know if push-ups could possibly help? I have heard both that it could increase OR decrease the size, so I am looking for a more clear answer.

They merely make them appear different, not change their size. Toning up the muscles can help with tone But nothing changes their actual size.

Push-ups are designed to give women the appearance of a more ample breast size or to emphasize what you already have. Often these bras will be in smaller sizes than what you would need.

I would go to the store and check out their minimizer bras. If you are in the US, Target has some, if in the UK, ASDA has some, as do most department stores. You could also just try on a variety of styles and see which ones you feel make a difference for you.