A twelve week old pup should not need a 2-week shut down, maybe one week, but socialization episodes should be kept short and positive and whether training or socializing, less is better, quit when the dog is still looking for more.
I agree that the dog was over-loaded and that he did not know you well enough for that level of trust. Try not to worry too much about it, and next time just go to the store or just go to the park. Take it easy.
Also, whenever you feel like you have no control over your dog, back away from whatever you are doing -- not literally. But if you felt you had no control in the parking lot, you should not have gone for a walk with the two dogs. Your pup needs to know you are in control. So, what I would have done was to at that point crated the pup in the vehicle and told my friend that I probably did too much with him already.
Don't feel too bad. l know that when I had a good time at one pet store, I went to another with the pup, and trying to get the most for my gas, I then went to a third. Then I talked to this woman for about 25 minutes while her child danced around and kept dancing toward the dog. Finally the poor pup had had enough and barked at the girl, it woke me up to what I was doing wrong.
RIP Arwen, CD RN CGC
RIP Whitney, RN CGC
Jenna, RN CGC & Babs, CD RA CGC HIC (not AKC)
Heidi, RA CGC & Tori, RN CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear