The best way to tell if your cat is pregnant is to take her to a vet for an exam. However, if you are correct about the ten weeks then she should have had the kittens by now. I recommend taking her to a vet for an exam and to get her spayed.
Good Luck
Vomiting can be for many reasons.
Upset stomach? Could he/she have gotten into anything? Ate something they weren’t suppose to?
We recommending withholding for for the day and starting to then feed small amount if they seem to be improving.
Next steps would be radiographs to confirm whether anything seems odd, and sometimes sending out a blood panel to check levels.
Let us know if you have any questions!