I know answers might not be what you actually want right now - skip this if you like. But assuming the ultrasound technician is correct:
How does this happen? Random chance. The likelihood increases as you age, but you may have been unlucky this time.
Why me? Random chance. It's not personal. Unless you're religious and it helps to think that you have been chosen as a strong person to give this special baby the care it needs for its life, however long or short that may be.
What have I done? Your best. You've done nothing to deserve this worry.
I had days where I couldn't keep folic acid down due to horrific vomiting for a week is it my fault? Absolutely not. That has nothing to do with this random genetic event. It's nothing you've done or didn't do.
What if I can't carry a baby that can live to full term? That's unlikely to be the case. The cysts on your ovaries could just be to do with the HCG/progesterone in your system at the moment and they might naturally resolve themselves in time. Or you might have PCOS, which might make it more of a challenge to have more children, but doesn't rule them out (my fried has PCOS and two children close in age).
Personally, I think it's outrageous you've had an US technician tell you this when she scanned you outside the recommended window. Any queries should have been reviewed and double checked by a qualified consultant. Which is what they will do with your NHS scan.
These measurements can be out if the baby isn't in the exact correct position, if the image isn't the right size on the screen, and (of course) if the calliper tool isn't positioned correctly. Even then, it's not a diagnosis until followed up with other tests. I am angry for you that they have left you high and dry after this.
Maybe you should ring the maternity unit tomorrow morning and explain the situation. See if they can see you sooner.
I will be amazed if this does turn out to be bad news. I think you have everything going for you for this to be a horrible mistake.