Well, don't be scared, it sounds like a minor infection. And try not to be embarrassed, every female has a vagina, and no doctor is going to be shocked or appalled to find out that you do too.
It could be a yeast infection, but since you haven't mentioned clumpy cottage-cheese type of discharge, it's more likely to be a bacterial infection. There is a common one called bacterial vaginosis (BV). Yeast infections can be treated with over-the-counter products, but if it is BV or bacterial in some other way, that takes a run of antibiotics.
Just tell your mom that you need to see a doctor, preferably a gynecologist rather than your pediatrician (unless you really like your pediatrician), because you think you have a bacterial infection in your lady area. (Be as ho-hum and matter of fact as you can when you tell her about bacteria and your symptoms, or else she'll be afraid you've been having sexual activity and are hiding it.) See if she can get you a gynecologist who is a woman; it helps a lot when talking about 'down there' to a doctor for her to also be female.
In the meantime, try some sitzbaths, and also wear only cotton underwear.
When you see the gynecologist, just tell her that your vaginal discharge has a really acid smell, and your lady parts are itchy and red. Your mom doesn't need to go in the exam room with you if it would increase your embarrassment level too much. (You have the right to ask her to wait in the waiting room.)
I assume it's nothing serious, but you do want to take care of things like that the right way. The doc will swab the area if she suspects a vaginal infection, and diagnose it properly. Take your full run of antibiotics if any are prescribed, don't stop just because things are feeling better.