回复：Urgent question about F1 work outside campus

我们学校的international center发现了这个问题，他们说，我只能暑假先回国一趟，再取得签证过来完成学业。

If you don't do what they say but continue to stay in US, your record will show that you violated your status (entered by 学校的international center), and you will have trouble changing to any non-immigrant status or adjusting to LPR under most GC categories, (including all EB categories) in the future if without leaving US.