In terms of germs, wash your hands while handling everything. That’s the rule in my house when someone is sick, wash hands before touching the kitchen, which includes just opening cabinet doors and the fridge. We almost never give each other an illness.
You are probably not very contagious if you have had a cold all week, assuming what you are calling a cold is actually a cold.
For me, your brownies are “sick” whether you baked them or not if you touched them with germy hands, because I tend to be over the top about getting sick. You still touched the package, So for paranoid me how are the brownies taken out of the package? I don’t expect you to answer that, I just have that running through my head if I’m at the party.
Are you touching serving spoons and drink bottles at the party that I am going to touch also?
If you’re sniffling and sick I’m worried about you getting me sick regardless of the food. I’d ask you how long you’ve been sick, and then I’d feel ok about it. More than 3 days I tend to not worry.
Since you are feeling under the weather it’s probably easier for you to just buy something though. I’ve become more and more lazy about these things. I often am invited to potlucks, and I actually cook about ⅓ of the time lately.