Yep, you inherited it. My x-husband, like your dad had grey in his 20's. In fact, one time when he was 26 he was on his way to an operating room for minor surgery and the nurse brought him back to his room because she thought she had the wrong guy.
My son who is 20 has about 20% grey. He started getting them in his teens. The other son, 22, seems to take after me without any yet.
Sadly, dying it is your only option. That's not that bad. My husband wishes he had hair to dye.

You will get people who mention it to you as if you didn't already know. Ignore those people. It's rude to point out things that people wish they didn't have such as grey hair, extra weight etc...