Definitely a hematology consult is in order; one of the key tests will be to analyze the peripheral blood morphology (blood sample on a microscope) and likely perform a bone marrow biopsy
to look for abnormalities in the production of blood cells. The arterial thrombosis
symptoms are quite unusual; you will likely have a battery of tests ordered by the hematologist
to look for abnormal causes of blood clotting, and likely (if you haven't already) be placed on a blood thinner. As you can imagine, to orchestrate all of this extensive workup, it is more practical if you are admitted to the hospital, particularly given the issue of the arterial clots.
Hope this helps
Mayo Clinic Rochester