Central to the implied intent of your question (the cause and the significance of the finding of blood in your mouth) is the uncertainty of the source of the bleeding. For example, a substantial majority of the blood found in the mouth is due to bleeding from the gums, and a majority of gum bleeding is secondary to inflammatory periodontal disease. This condition is usually well-managed by a combination of professional cleanings by a dentist, patient compliance with a rigorous regime of oral hygiene, and (sometimes) surgical intervention by a periodontist. In some cases, gum inflammation may be a result of temporary injury, as may happen in the course of crown service, so your suspicions that this may have some relevance is justified. If the crowns are indeed the source of the problem, the delivery of the permanent crowns should allow any gum inflammation to resolve, assuming those permanent crowns were properly designed and fabricated.
However, if your perception that the source of the bleeding is in your throat, this would have very different implications. Blood from the throat may arise from either the respiratory or digestive tract, and it usually signifies more serious disease. For example, lung infection, erosive esophagitis, peptic ulcer disease, or esophageal varices secondary to portal hypertension may all theoretically be a source of blood in the mouth or throat. Disorders of clotting or other hematologic disease may also account for blood in the mouth, especially if accompanied by more widespread bruising or constitutional symptoms.
Even so, a majority of oral bleeding is relatively trivial, so your first stop should be to visit your dentist to assess for periodontal disease, if the bleeding continues for more than a week or is substantial in quantity. If this fails to disclose a cause for your bleeding, you should arrange to see your primary care medical doctor for a more formal checkup.
Hope this helps...