chicks hatched from infected eggs contagious?

I'm not sure- did they say what the infection is?

It might be to late if you are not using quarantine procedures... please strat proper QT procedures if possible.

QT procedures:

Work with established flock, come in change clothes and shoes,

work with new flock- do NOT go back to established flock

put all contaminated clothes to wash (what you were wearing with the established flock, and what you just wore with the new flock, dip shoes into a water/bleach solution if they can handle it, water/white vinegar if not)

Shower and blow nose- also wash hair.

If possible stay away from all flocks for three hours (give or take) most but not all microbes have a limited 'outside host' life.

You cannot use the same food bowls or water bowls between the flocks, you should not handle food or water bowls for one flock while 'dirty' from the other flock, use different scoops and food containers if possible.

The next time (next day) you need to do things for your birds always do the established flock first then the new flock and don't return to the established flock w/o washing and changing clothes. (this might allow pathogens to transfer TO the new flock FROM the old flock, but not the other way, if you want FULL QT you would need to shower and wash hair, blow nose between each flock. (I don't do that- just one way QT for me)

Old birds and new birds should not share air if possible for at least a month, that month starts over every time one of them is sick, even on day 29- if a chicken has a sneeze or cough or discharge from the nose the month starts over at day one.

I feel it is my responsibly to the lives already in my care to not allow them to become ill from new cute creatures- this is how the FL rat community prevents disease from transferring into our pet rats, it is the same for the birds

I am so sorry this happened to you- hope it all works out.

I'd try to find out what infection they are talking about.  Some diseases  are indeed passed from the mother hen to the chick through the egg -- I would have to look each one up, but I believe those are all viral diseases, not bacterial.