My baby is sick. Is it my fault?

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He has been fussy all day yesterday, and now he has a runny nose and he's feeling very poorly. He is crying in his sleep too 😢 I don't know how to help him, and I feel like its my fault, I should have put him in warmer clothes, or not have gone out with him... I take him to his pedi today, but I feel so bad... He is only 6 weeks old...