As to the bloody sock, don't give this a second thought. Imagine how many people have some sort of procedure on their foot/toe and then travel and therefore present with a bloody sock. Just note it to the Officer and it won't cause an even remote issue.
As others suggest, there should be disposable socks available at the checkpoint, but in your case, I would pick up a pair of surgical / industrial booties (cost a couple of pair for <$1) and use one of those to walk through while the shoes go on the belt (I am presuming that you don't have Pre-Check).
You could certainly ask to remain seated and to have your shoes run through separately, but that does mean a full secondary for you and that seems a lot of hassle all to avoid what really isn't anything to be concerned about. Or if it is, it is a TSA problem, not yours.