Cute puppy! My Puppy, Cassie, is about the same age. It all sounds familiar. I held back on taking her anywhere, but to her vet, until my vet gave the okay (no neighborhood walks either). Vet suggested waiting 2 weeks after her vaccinations were complete before going out in public, so I complied.
When we went out in public with walks around my neighborhood and walks in the park, she barked a lot. Traffic noises, seeing herself in a window reflection, other dogs, people, etc. - all prompted her to bark. The first time she walked into her vet's office (instead of being carried, which was the case for her first trip) she barked so much they put us in a side room and removed us from the busy waiting room. Once she quieted down, they forgot us, until I peeked out of the room and inquired, LOL
It's slowly getting better. We are 3 weeks into walking in my neighborhood, and so far this week, she hasn't barked. She is most apt to walk at the beginning of a walk.
We started an obedience class last Sunday. There are a least 15 dogs in the class. Cassie barked a lot, when we arrived. She eventually settled down, as we worked on our assignment. During the break, we walked around some of her classmates and her barking decreased, as she and a few receptive classmates sniffed each other.
Hang in there, it does get better. In my experience, the more I continued to expose her to the things she was barking at, the less she barked. I'm still working of barking at home. When she hears neighboring dogs bark, she tends to get "her bark on" - work in progress.