Antibiotics have been know to affect
liver enzymes, in both a hepatocellular
and cholastatic manner. Amoxicillin can do this even after you've stopped taking it, but this is uncommon. Do you have any other symptoms like joint pains or rashes, no mild allergies to antibiotics?
Also, vigorous exercise can cause elevations in your AST levels as well, as you suspected. This may account for the elevation bias between the liver enzymes.