My son is a HS senior RHP who has loved pitching since age 10. In the lower levels I don't remember feeling very nervous. Even when he was a HS freshman pitching for JV I don't remember feeling more than a slight, brief nervous feeling. But when he was a barely-16-yr-old skinny soph pitching HS varsity against 18-yr-old young men, my stomache started doing flip-flops! I was so nervous that I couldn't sit in the stands, had to find a quiet place to sit off by myself where I could barely see the action but no one could see me.
It has gotten gradually better over the past two years, but I still prefer to sit on the 1B sideline far enough away that my son would not notice me if he did look (although he says he does not notice anything not on the playing field). And I usually write down his pitch count just to keep myself occupied. Dad stands quietly next to the stands behind home plate, if possible ... watches all the pitchers, and chats with other players' dads between batters.
Son also plays position when not pitching ... at those games, I'm just a happy spectator in the stands! His senior HS season will start in about 5 or 6 weeks ... then next year I'll have to adjust to him playing college ball! That will be a thrill, and I hope we can make it to every home game, only about 90 minutes away!