gemly, how often do you palpate your testes? Are you familiar with their anatomy and that is a new finding or you think it is something that was there and you probably hadn't noticed before? If what you feel is identical on both testes I'm inclined to think you've stepped on your epididymis, they fit the description well. Search for it on wikipedia and look on the immage if that can be what you found.
If you still it's concerned and think it can be abnormal you can always go to a doctor like you said. Doctors are trained to deal with these issues and there's absoluttely no need to feel embarassed with them. You probably also don't need to feel embarassed with your parents, but if you still do just do as you suggested because doctors keep confidentiality of their patients.