Well, it ain't a brown recluse, 'cause you would be feeling really bad by now.
Are you allergic to wool? Some random bug in the hat? Was the hat washed, dry cleaned, or treated with any new chemical prior to storage? Have you seen any more red areas since removing the hat? Are the red areas spreading or getting larger?
I wouldn't wear the hat again, in any case... A good dermatologist should clear that up in a jiffy.
Guitars:
Fender 2006 MIM Fender Stratocaster HSS in 3TS
Ibanez RG 570 with a bridge Invader
ESP M II Deluxe with a Tune-o-Matic bridge
Eleanor, the magical, mystical Road Worn wonder Tele
Blackstar HT Club 40