no and no. I see this pt almost ever shift. first trimester bleeding is not emergent unless significant or associated with pain. many ob's work this up in their office if pts think to call them.
ER workup is pelvic exam, serum hcg level, wet mount/gc/chlam if d/c suspicious for pathology, and an u/s, especially if concerned about ectopic, tubo-ovarian abscess, or torsion. add an h+h and a t+s or t+c for significant bleeding.
I have never had an ob doc ask me for a progesterone level out of the ER for any indication.
remember may women do have a bit of spotting in the first trimester as the fetus implants to the uterine wall. this bleeding is called hartman's sign and usually occurs around week 6. some women mistakenly count this as their last period so their dates are off by six weeks or so. also nl physiologic vag d/c tends to increase in pregnancy. any concern for infection obviously merits an eval.
we do too many evals of first trimester spotting in the er at a very high cost. this really should be done in the ob's office unless there is concern for ectopic, etc