My 2nd ds had bloodshot eyes for a while, it took a few weeks for his eyes to Fully clear up if I remember right... I don't really know why exactly, I think it had something to do with the birth. I am sure someone else could be more helpful.
Just one spot in one eye? Bea had this too. They told me it was from excessive pressure during the birth (I swear I wasn't kegelling! ). It did clear up... I don't know when. She still had it at her shower and that was at 1 mo. Probably not too long after that.
being born is hard work. My guy looked like a he'd been in a prize fight for quite a while just from being pushed down in the birth canal for such a long time. I guess if you're really worried you could ask your ped.