Hi T., If it were the vaccines then he would cry in your arms and out of your arms. If he stops crying when you pick him up then it's not the shot.
At some point babies learn that when they cry that they are picked up and will do so.
He could also be having anxiety due to the pain at the time of the shot, and I'm sure you picked him up right afterward which he realized. Don't think these little sweetie aren't smart enough to figure this out.
Before you get to worried about the vaccines, ask yourself if he is doing this all the time or just when you go to put him down. It will not hurt him to cry for a small amount of time. My daughter sat in her front room and let her baby cry for 10 minutes and he finally learn that when she puts him in his crib, it's time to sleep.
It's very hard to do, my daughter cried, but she knew that if she didn't do it that she would have to deal with it for some time to come. It's not fair to her and her husband that should have time to themselves after a very long day of caring for her son. If you keep thinking he's hurting and picking him up, you will be doing this for a very long time.
If he was hurting he wouldn't stop crying when you picked him up. So know that he's not hurting, he's just learned how to get you to pick him up. It's a hard lesson to learn. I'm a mother of two grow children that learn it too.
I love being a grandma now, just know that it does get easier. Remember that after the storm is a rainbow.
Love and Light,
Rev. G. Hudson, Reiki Master.
www.reikigailhudson.com