The link I posted above to dieworkwear / the menswear guy has information about animal shelters. I updated my post with a preview screenshot. Please click through to see the details.
Welcome to Chicago! Sorry about the weather, the cold just landed about a week ago, and the snow came last night. BE VERY CAREFUL of black ice under the snow, on bridges and underpasses, etc.
If you are in need of relatively affordable warm clothes, check out Uniqlo. The warmest tier of Heattech long underwear is fantastic and may be enough to augment whatever you managed to bring with you. The Men’s Ultralight Down Jacket is still on sale for $70. I picked one up recently and was extremely warm wearing it and a wool t-shirt on a walk to the post office in 20F weather similar to today. The jacket seems a bit on the flimsy side, so if you expect to do a lot of walking with a backpack you may want to look for something more robust or toss something like a cheap rain poncho on over the jacket and under your bag straps.
There is a Chicago thread you may want to check out when you get some breathing room.