Is there a blood test that can tell if my spleen is enlarged?

No. Spleen enlargement may be found by physical exam or imaging. Splenomegaly can be caused by liver failure or itp. Low platelets should raise suspicion of an enlarged spleen due to the aforementioned conditions. Mononucleosis diagnosis may involve eval of spleen.
No. Generally if it is big enough, a physician can feel it on physical exam. Ultrasound or a ct scan would also be able to tell how big your spleen is.