Kellxx- I agree with a couple of the others here, I really think you should make a formal complaint about it as obviously the surgeries procedures and protocols for handling vaccines aren't stringent enough. It is good to know that the vaccine administered isn't dangerous to him, but I'm sure plenty of other vaccines in the surgeries fridge may have been.
I'm really happy to hear that little Jesse will likely be fine from the incorrect vaccine (other than the usual possible side effects). Poor little bugger about needing to be re-vaccinated tho!

And big hugs to you - you've had more stress than a new mum needs today.