What can I do about my sagging mouth corners? I'm only 19 and It's getting worse and worse every day! (photos)

Thank you for your question.  This is a dynamic area of the face and the position of the corners of the mouth are controlled by muscle activity, suspensory soft tissues, gravity, bony framework, etc.  A full exam would be necessary, but you may benefit from something as simple as a couple units of botox on each side to the depressor anguli oris (DAO).  This muscle pulls the corners of the mouth downward and weakening it will allow the corner to preferentially raise.  See a facial specialist in your area so they can give you a detailed exam and make recommendations for your individual anatomy.  All the best!

In my opinion surgery is not a good option for droopy mouth corners unless it is an older individual who is getting a facelift which can improve this problem. You are young and as you said it it not so bad. I actually don't see sagging in your mouth corners from your pictures. The corner of the mouth is a very complex structure and is controlled by several muscle groups. Sometimes in the way we animate one muscle can be more dominant and in your case the muscle the depresses or lowers the corner of the mouth could be overacting and pulling down the corner. This can be improved with targeted botox injection into that particular muscle. usually very low dose. 

A temporary improvement in drooping mouth corners can be achieved by Botox injections. A more permanent procedure is a small surgical change in the position of the corners of the mouth known as a corner of the mouth lift.