。
It's been ten days since my boyfriend was put in the holding cell.
Literal
Boyfriend [subject-が] holding-cell [target-に] entered-[and-て] 10 days passed [polite-past-ました].
A te-form chained sentence with a clear temporal structure. 入って ('entered, te-form') connects to 経つ ('to pass [of time]'), specifically conveying 'X happened, and (since then) Y time has passed.' This ~て+期間+経つ is the standard way to talk about elapsed time since an event. 留置所 specifically refers to a police holding cell (短期 detention), not a prison (刑務所).