Before anything else, start muzzle training immediately. It's essential to get the correct muzzle size to avoid discomfort, and properly condition the dog to accept it. For help with these please find advice on the Muzzle Up, Pup fb page (link below). Yes a small dog seems much less threatening than a large one, but even a kitten could cause significant eye damage from a scratch, and it's not worth any potential injury to your toddler.
Everyone has different ideas of how to define aggression and I personally believe there are only 2 ways a dog is truly aggressive. Either someone has trained them to attack for no reason other than to cause harm, or the dog has a genetic predisposition/neurological issue causing this behaviour. Everything else I believe is reactive behaviour and almost always comes from a place of fear.
I may be totally off because it's impossible to assess from just a few short descriptions but amongst many other things it sounds like your dog never got the exposure needed to build up his own confidence, was probably quite comfortable in his own little safe bubble at home until a screaming baby came along, and has never been able to adjust to the unpredictability of a tiny human. If he's living every day way over threshold this will be extremely stressful and miserable for him. I'm unsure why your vet offered medication unless they believed there was a neurological problem. Training will only help if there is consistency - and by consistency I mean you have to start from scratch, eliminate all triggers and very slowly build up at your dog's own pace. This would be hugely time consuming and require a lot of adaptation which may not be realistic with your family situation. Is your child/environment the main trigger? Keeping them separate may not be enough if he can always hear a noisy toddler and is never able to properly decompress and relax.
I think this is 100% a rehome case and not euthanasia. In the right environment this dog could be completely different. How did you find these potential adopters? It sounds like you have a lot of reservations which might mean already it's not a good fit. As others have said, try to go through a rescue who will do checks to ensure adopters have relevant experience to cope with this behaviour and an environment that would best suit him. He may not necessarily need to be an only dog, it depends on many factors such as the temperament of other dogs and how slowly owners would integrate him into the family.
Chihuahuas are not naturally fiesty, yappy, mean dogs. They have breed characteristics and tendencies like any other but it's the way so many people treat them that often enables and enhances this behaviour. Things like (and I am not implying these are things you've done OP, just generally speaking) picking up and physically removing the dog from situations they don't even get a chance to process themselves and make their own decisions on how to react, or encouraging all sorts of guarding behaviour through praise at the wrong time. They need freedom to explore and express what it is to be a dog and be able to think for themselves, or they end up a ball of anxiety and feel the need to defend themselves from everything.
If you are still considering keeping him or want more advice on rehoming you can find lots of help on the fb group Reactive and Aggressive Dog Support Group (link below) from people who have been in similar situations. I know it would be very difficult to let him go and only you can decide what is right for everybody. I wish you all the best and hope for a happy outcome for everyone 🐾
https://www.facebook.com/groups/muzzleuppup/?ref=share&mibextid=NSMWBT
https://www.facebook.com/groups/1106588519404354/?ref=share&mibextid=NSMWBT