I caught measles (not German measles) at 10 weeks with DC2 back in 2008 from DC1, who was just about due to be vaccinated.
I'd had measles as a child AND been vaccinated. I fell into the small percentage of people who get it regardless, however I had enough antibodies to get "modified measles" which is a mild form.
The vaccines given in the 1980s and before only provided 90% immunity to measles (not sure about rubella or mumps) which is why these days children have a second booster not long after to make it up to 99% immunity. I guess I fell into the first 10% and then despite catching measles clearly it still wasn't enough! I also had rubella twice as a child before vaccination, but I do have the antibodies now.
There's very little research on regular measles in pregnancy because vaccination has pretty much eradicated it aside from the odd outbreak here and there, so at the time it was very hard knowing what might happen. Research papers I found ranged from a 1 in 100 chance of something going wrong to a 1 in 3. Not very reassuring!
DC2 was fine as it happens. In fact because measles in pregnancy is so rare, I asked a research hospital if they wanted to see if DC2 had antibodies (i.e. had it crossed the placenta?) so I got her tested. She wasn't immune so clearly she'd never even been touched by it.
Rubella (German measles) is another kettle of fish altogether, but most girls were vaccinated at school I seem to recall. It's one of the things they test for with your antenatal bloodwork as well - they would tell you if you were not immune.
Chicken pox is, I think, only really risky if you have it around birth, but don't quote me on that. Most people are immune though having been exposed at some point before now.
Find out if it is measles or German measles if you can - only German measles (rubella) is tested for with your antenatal bloodwork. And ask your parents if they're available to be asked if you've had chicken pox.