Uterus didelphys is rare, but it isn't the end of the world. In the future when you want to have children there are increased risks. I always knew I had a septum in my vagina, but I hadn't been diagnosed with uterus dedelphys until last year after an ultrasound. I have been getting pap smears for 15 years, and no one ever noticed I had two cervixes as well. It was always hard for ob/gyn's to find even one cervix, let alone two. When you do find a ob/gyn who you trust make sure they look for a second cervix.
There are many many women with uterus didelphys who still have healthy pregnancies and deliver heathy babies. It seems like the most common risk is that the baby runs out of room to grow and comes early and often breeched. I have been told that the risk factor is similar for a woman pregnant with twins.
Even though you feel embarrassed it's a really good idea to have regular checkups. Probably the best thing to do is to schedule a consultation and make it clear when you make the appointment you do not want an internal exam, then talk to the doctor about your fears. Tell him or her you have never had an exam. Then, provided you feel comfortable with them, schedule another appointment for a screen. In most practices, they will have a female nurse present. You can also see a female dr of course. No one likes internal exams, and everyone feels some anxiety, but it's important for you to get a gynecologist that you can trust. If they are a good doctor they will talk to you about what they are doing and try to put you at ease. Cervical pap smears are recommended every year or so for young women, and they do save lives, even though it's rare for women of your age to actually have cancer. But these checkups get more important as you get older. Do it, put your mind at ease, and it probably will not be as bad as you think it will be. Also, consider getting a book from the library on female health that explains exactly how the internal exam is done, to put your mind at ease.