Feeling concern over my puppy’s lack of socialization

For some (incredibly long) context:

My partner and I adopted a mixed breed puppy from our local shelter a little over a month ago. At that point she was estimated to be around 10 weeks old, they didn’t know for certainty as they had just found her roaming the streets with her two litter mates. They believed her to be a GS mix, we found out later through Embark that she is majority Old English Sheepdog, Golden Retriever and American Pitt Bull Terrier with some other breeds as well. When we had adopted her she had been vaccinated and spayed by the shelter, they informed us she would need her second round of vaccinations within 3 weeks. We made an appointment with our primary vet for a wellness check and they said everything looked good. They advised us to limit interaction with other dogs and people as she settled into her new home and due to only having first round of vaccinations. We took her on a few car rides and had her meet a very limited amount of people in our home (2 other people). At 13 weeks is when she received her second round of vaccinations, but here’s where things take a severe turn. A day after her vaccinations, she choked on a piece of kibble and started to asphyxiate. We rushed her to the closest emergency vet who started her on oxygen therapy and took x-rays. They were alarmed to see her lungs filling with liquid and had cause for concern over a collapsing lung (thankfully it wasn’t!). They sent us to another emergency vet who could scope her, she was on oxygen the whole time. She was with this vet for 48 hours on oxygen therapy and antibiotics. They expressed concern over aspiration and non cardiogenic pulmonary edema. She was sent home in which she was on mandatory rest and could not play, run, go out, or meet anyone new as to not cause excitement and over exertion. A week after, we went back to her primary for a eval and more X-rays, they concurred that she had pneumonia and needed to be on antibiotics and more mandatory rest for at least another week. This is putting us closer to current day, where just a few days ago she was cleared of pneumonia and given her (partial) third round of vaccinations. I say partial because the vet did not want to overwhelm her body from just being on antibiotics, fairly and humanely we agree. The issue is she is still without her rabies and one more shot. The vet is continuing to tell us to refrain from socialization. My biggest concern is just today we took her on a car ride to the grocery store, she barked and lunged (in the car) at everyone and everything. She keyed on every movement, every sound, and barked at laughing children. I’m hugely concerned as she is now officially 16 weeks and I feel like I’m failing her. The vet offered to recommend behaviorist trainers but the ones in our area are booked out. She has met two fully vaccinated adult dogs and did great with them, and is great with people who come into the home. But outside it’s a different story. Is it too late? Can anyone give insight into what my next steps should be besides waiting to meet with a trainer? Any advice or suggestions are greatly appreciated!