I got a flu shot this year but...?!

Yes you can or they contracted it from someone else.

Just because you are immune to something does not mean that you are not a carrier of a pathogen and can pass it on to others.

I have a degree and work in health care.

No. The flu shot contains inactive strains of flu, not live flu virus. You can not get the flu from the flu shot, and you are not contagious to others as a result of getting the flu shot. However, since the shot only protects you against a few strains of flu, you may still get a strain of flu that is not included in the shot.

That's very possible, I work at a daycare( I have the flu shot as well) and I never get sick and some of the children don't, yet their families and my families are sick all of the time.