I now take a daily tab of Clopidogrel, a blood thinner prescribed after my TIA this last spring. I freely (and sometimes most unconveniently) bleed from the slightest cut, graze as well as injection sites. This does seem to not only be normal but fairly essential for my wider health needs to keep taking this medication. I rarely need to apply any pressure after that bleeding; I just give a mild wipe of the drop of blood that is appearing g and that seems to stimulate closing and healing process. Just awkward cuts, such as a paper cut on a finger, seem to need a sticking plaster. It's all slightly weird, needing a change in response to any cut, after 70+ yrs of never needing to bother.
I also now bruise, very easily; such bruises include at injection sites, particularly if I tremble or shake while injecting and counting to 10! Some of my bruises I can't explain, ie I have no recollection of bumping into something, etc.