Removing Lint From Towels?

I was in a hurry and pulled our pastel colored sheets off the bed and tossed them in the wash with Tide and Downy. There was extra room so I tossed in some white towels (they are about a year old and do not shed). When I went to put them in the dryer I noticed a medium brown towel was in the mix. It's a few months old and just stopped shedding. I thought it would be alright, then the last thing I pulled from the washer was a wine colored fuzzy throw. I didn't see any wine colored fuzzy stuff on anything so I just turned on the dryer with Bounce dryer sheet(s).

Everything came out looking great. It wasn't until I used one of the towels that I noticed it left wine colored fuzz on me. You can't see it on the sheets or towels, but there is an invisible fuzz waiting to stick to you if or when you are drying off. Sorry for the play by play, but I didn't want to leave anything out. Is there anything I can do to remove this invisible fuzz?