COVID vaccine?

I’m in California and as of March 15 I may be eligible for the vaccine as a pregnant woman. My OB says it’s most likely safe because it’s not a live vaccine, but I’m hoping to hear from any of you who have had the vaccine yourself. Did you have any complications? Did you get a fever after the shot? I’m so conflicted because I’d love to be vaccinated before going to the hospital in April to give birth, plus it would be wonderful to give some immunity to my baby, but I’m nervous because it’s so new and untested on pregnant women. If I wasn’t pregnant I would 100% get the vaccine without hesitation, but I don’t want to put my baby at risk either!