Is it possible the doctor is wrong about my baby's sex?

Depends. Features of gender are fully developed by 12 weeks but few are ever confident predicting sex by ultrasound before 18-20 weeks.The equipment used and skill of the examiner are variables.Male parts may or may not be displayed during the exam, so at best it is a learned guess. I don't paint the nursery based on an ultrasound.There are also rare conditions where sex is not easy to assign even at birth.
Is the baby born? If your child's is born and you have concerns, make sure they are addressed. You can ask for a "karotype" which will give you a definitive answer. If unborn, then wait for the surprise at birth .
Absolutely. Short of dna testing, there is plenty of room for error on predicting the sex of a baby using ultrasound. Operator error, interprtation error, the anatomy of the baby and other factor can contribute to a false identificaion of the sex of a baby. It is what it is however and in the end, we find out and nothng we are going to do about it.