Ask, repeat ask, the Doctor. Post-surgery treatment (or not) can vary, can vary with after-tests, etc. Yes, go on, but check annually or more, if Doc says. They monitor the first year closely.
18 years after my prostatectomy and they still want a yearly PSA, all have been negative. Not sure how works with Medicare, or if it is the Insurance or what that pays, but it is part of my Annual Physical, maybe was prior to the diagnosis. In other words, whoever/whatever is paying for your Annual, it probably covers it. The PSA wasn't what clued them in, initially, on me. As an old fart, I suspect they will stop bothering to tell me to get it. Once you reach 75, I guess they figure it doesn't matter, since you can drop dead tomorrow.
Under the "new" standards, I'd be dead if I hadn't had the tests/exams until waiting for the "recommended age". To use an unfortunately appropriate phrase, that new standard pisses me off.