My son is sensitive to dairy. When he was a week or two old, we started noticing hives immediately after he nursed. Knowing dairy is a most common allergen to infants, I cut that out and the hives immediately went away. He never had blood tinged poops, but would at times have mucus present. And he was really gassy, although I thought that was sort of normal.
Fast forward a few months...a few weeks ago I ordered a sandwich and cheese was present. I swallowed a whole bite before noticing I ate cheese. I breastfed my son and there was no question he reacted to the dairy - he *screamed* and cried. Heartbreaking. From eating the cheese through to him breastfeeding, probably 2 hours had passed.
I'm treating that bite of cheese as a food challenge. At least now I know he's still sensitive.
So yes, it sounds like something you're eating is bothering him.
Don't know about the red bum though.
Good luck to you!