First of all calm down, this is actually common and it happens to all girls at some point in their life. This starts to happen around six to twelve months before a girl starts her period and enters puberty. This discharge is a way to keep it moist down there and fight off infection, so it's nothing to freak out over. From your description, your discharge is very normal and it just shows that you are healthy and that you are growing up. Yes it's supposed to be white and dries up as yellow, and yes it's supposed to smell kind of bad. You will continue to have this discharge until you enter menopause when you are around 40 or 50, so it's about time you get used to it because you will be seeing it for many years to come.
Second of all, you can go and talk to your mom. It's okay to tell her about this. She will understand because she is female too and has experienced or is experiencing what you are going through. I also doubt she will go around telling people; this isn't something people often gossip about because it's SO NORMAL. Why would your mom go tell other people about something that is normal? Does your mom go around telling your neighbors that you can walk? That you can talk? That you have arms? Of course not, and that's because that is something common. The same thing applies to your discharge.
Third of all, don't be afraid to ask your doctor. If you ever feel like there is something funny going on with your body, your doctor is probably the best person to talk to, because it's their job to help you take care of your body. They won't think you're stupid, think you're gross, nor would they get mad at you, so there is nothing to be afraid of. But in this case, you don't need to go to the doctor because what you're going through isn't weird or wrong.
I understand that you might feel uncomfortable talking about something that seems so private. But you have nothing to worry about. Every female knows that you're talking about so you are not alone, therefore there is no reason for you to feel embarrassed. Instead, you should be glad because, like I said before, it means you are a healthy girl! Being healthy is very important, so you should be thankful for that.