Yes, I agree, one vaccine at a time is best for these little ones. As someone else said, the "L" one is most likely Lepto and that vaccine in particular is notorious for causing problems (not in every dog of course, but it's quite common). Please get him to a vet and give us an update when you can
Just a side note - any vet that "asks" the owner what vaccines they want is a
in my book. It's good in one way that he checked with you before giving anything, but I'd find another vet for future use cause that sounds strange to me. Plus most good vets won't give that many vaccs. to a small dog in one day.
Hope your baby's ok and we hear from you.