PCR tests aren't necessarily positive for months, it depends on the level of infection and viral clearance (either directly, or from dead and dying tissue). While PCR is exquisitely sensitive, the machines used in these assays basically measure the rate of amplification and use that to derive the amount of viral RNA in the sample. There's a minimum sensitivity to avoid false positives. You can be clear in 10 days or so.
I'd take a self-administered test about a week before and see if you are clear, at least that might remove a surprise. Otherwise, this is travel in the covid era.
