The university I am applying to has an option in which I can upload my under review/accepted papers. Is it okay to do it considering the fact that the paper is not published yet? My under review paper has the same topic as one of the research topics in a lab in that university.
If the university says it is fine, then it is fine. Label them correctly, of course. But even if they don't specifically ask for them then a person can submit them as "under review" and it will be properly understood. One might even list work that is well along, but not yet submitted as "work in progress".
Just be honest in labelling. And for those under review, say which journals/conferences are currently reviewing them.