Can you get pid without having sex?

Yes: There are cases in other countries of tuberculosis causing pelvic inflammatory disease and Fallopian tubo-ovarian abscesses. Here in the USA however, the number one reason is sexual engagement with intercourse.

Yes but rare: This is complicated. Most PID is due to chlamydia or gonorrhea. Sometimes both are absent but it's still an STD from unidentified germs. Some PID is triggered by bacterial vaginosis, which sometimes is an STD but not always. PID and silent chlamydia lead to more PID, so some cases aren't STD now but are related to past STD. PID entirely unrelated to STD is rare and it's extremely rare in virgins.