Do push ups bras cause sagging breasts? I'm 18

Not usually. It is important to support the breast to limit sagging. However, many factors influence sagging. The larger the breast the more sagging even with support. The quality of the skin is important as are hereditary factors that are not in your control. It is always better to wear support.
No. No, there is no evidence that any type of bra causes “sagging”. On the contrary, it makes sense that the use of a supportive bras may help prevent the effects of time and gravity. Of course, significant weight fluctuation and/or pregnancies may also cause breast ptosis (sagging). Genetics may play a role as well. Hope this helps.