I haven't started taking aspirin yet. She mentioned it when she initially prescribed it (5 months ago), and I hadn't started getting headaches at the 1-month follow-up visit, so I didn't ask. I have a follow-up with her in a few weeks and I will definitely be talking with her more about it then.
It isn't the injection/liquid, itself, that thickens the blood. T causes an increase in RBC and platelet counts (over time - the cumulative effect, like you mentioned) so this is what thickens the blood.