Lmp aug 14 for 4 days. Last intercourse aug 12. Period was unusual. Pain in rectum and vagina. Diagnosed pid. Could this be mistaken for pregnancy?

PID vs Pregnancy. So your doctor diagnosed you with pid and likely started you on oral antibiotics. In the course of this workup, I am hoping that they did a pregnancy test. If the test is negative, then this is not the issue. In answer to your question, yes a patient could be assumed to be pregnant when pid was actually the issue. This would be sorted out with a pregnancy test, an exam, and an ultrasound!
Probably not. With your last period being unusual for you it is possible you are pregnant but not very likely. However you can check a pregnancy test to be sure. It is common for a woman with pid to have unusual bleeding and more pain than usual. If it is pid then the pain should start improving as you take antibiotics.