Could doing push ups increase breast size?

No: Push ups will help tone your chest muscles(pectoralis). It will not increase your breast size.

Exercise...: Do exercises that are meant to increase the size and strength of the pectoral muscles (both pectoralis major and minor). This will enlarge the muscles beneath the breast tissue. Aside from that, you can use augmentation pads in the bra, but that just increases the appearance. Breast tissue consists of modified sweat glands packed in fat - you can only increase fat tissue by gaining weight.