#1 congratulations on your lovely newborn!
#2 you say that you are nursing a cold, and obviously your child will be exposed to the same germs so also might come down with a cold soon? Personally, that would be a reason right then and there for me not to attend, because I am sick. Although this time of year, not a lot of people have the luxury of staying home when ill because a lot of people are ill. Of course that's because they don't stay home.
#3 your baby's 23 days old. Honestly, I think if I had a 3 week old baby I would not be exposing them to a room full of 30 people who may also be nursing colds or other things and more than likely would want to touch the baby at least a little.
#4 you're suffering from a little bit of postpartum depression which is completely to be expected and you admitted that getting out, doing something social, that makes you feel better. You should definitely do things that make you feel better. All the time, but especially now, being pregnant for so long and giving birth and postpartum, it's a lot on you. Do something kind for yourself but I'm not 100% sure this is the right thing.
#4 if you were not sick, and if you weren't concerned about your baby. Being so young and being in an indoor possibly germy environment, then I would say that bringing a baby to a baby shower is entirely appropriate. I mean maybe not a wedding shower, maybe not a birthday maybe not a funeral, but a baby shower? Damn. If people are offended by crying or fussing or nursing or having to quietly interrupt the party flow because the baby needs something, or any diaper smells or anything else, then a baby shower is not the right place for them to be.
#5 some groups of people absolutely don't much care about germs. And other people care a lot! Like, I know people who if you express any type of concern about the amount of people in a crowd, or the amount of spacing between the people, or the fact that it's difficult to wash your hands, they'll say so what? So what? Okay.
I know other people who can be in a nearly empty store, if they hear one person in the distance cough or sneeze, they'll put down their shopping and leave the store. Like, seriously. I've noticed that a lot of parents with young kids have just learned to accept the fact that with kids, germs happen. There's no getting away from it especially once they become daycare/school age. It's inevitable.
All the things you mention here, myself, I'd be least impressed that you showed up because you're nursing a cold. All the rest of the things, although I might be concerned that your extremely young baby is exposed to other people's germs, I would say that you should come. Especially if you personally feel that you could use the social outing.