Yes your primary doctor can for ESR and CRP. They could check for Fecal Calprotectin but sometimes that is denied by insurance, so it might be better if your GI orders the test, so someone with experience can appeal for it to be covered.
But if you have IBD or think you might be flaring, you need to be in touch with your GI. Your primary doctor can't really help much in this situation. A primary doctor should not be managing IBD.