Help! Pregnancy + Employment advice!

Hey, mamas. Looking for some advice and hoping there are some legal minds/creative thinkers in here.

Recently got a job offer working with a counseling org within a hospital group. I’ll be working with youth 5-20 years old. Currently in the hiring process with a start date of Feb 10. Did a full physical, went over immunization records, and they found that I need a Varicella vaccine which deals with chickenpox immunity, though I’ve had chickenpox I’m not immune or something. My midwife confirmed this in December. I’m currently 16w pregnant and my future employers don’t know, as I was planning on getting through a few more months before having that convo. I’ve called my healthcare team and the vaccine is NOT SAFE while pregnant.

What the hell do I do?

Legally they can’t not hire me because of pregnancy but I’m worried they may claim a safety issue or something. Currently unemployed as I’m a recent graduate and need this job. I’m not super knowledgeable on the law behind this situation. I don’t want to say I’m pregnant because I’ll only be in this job for another 4ish months before maternity leave. I’d like to establish myself first. How do I get out of this??? Any help would be so welcomed!

I’m a Massachusetts resident for reference!