RedFishFool
It is natural.
Quick story...
i have been involved with baseball in many ways for most of my life. I had two sons that played professional baseball, one was a position player, the other a pitcher. He (the pitcher) was on the very first DBack team. I never got very nervous when watching position player son. But when he got called up I went to Arizona to watch. I was sitting next to Bill Olson, another baseball lifer, whose son Greg was a veteran who had 250 MLB saves.
Anyway, they were playing the Astros and tied in the 7th inning when they brought in son to pitch. All of a sudden I became a nervous wreck. I asked Bill Olson if he felt like this when he first saw his son pitch in the Big Leagues. Bill said, yes I did and I still do every time he pitches. BTW, Bill is recognized as one of the best pitching coaches in the country.
I suppose some people can simply enjoy watching, but I assure you there are plenty of us out there shaking in our boots. My suggestion is just try to act normal even though your gut is turning. Understand that everything is completely out of your control. In fact, that is the reason we get nervous to begin with.
BTW, my vote for the most nervous dad we have seen would be for Eddie Kazmir, Scott Kazmir's dad. He looked like a guy that had just chugged a 5 gallon pail of coffee before Scott pitched. It is a good thing that the pitchers don't feel the same as mom and dad when they are on the mound.
Bottom line... I think you are normal! Your son has a great arm, I hope he stays healthy and has a lot of success. He certainly has the talent.