Being an Umpire for baseball I see the different levels of talent on the field. I umpire High School, Legion, Summer College leagues, and Mens leagues. Let me tell you, If you think you could practice really hard right now for say 2 years and think you could step onto a MLB diamond and be, lets say, just a utility guy, you are wrong. It is not possible.
Being a Professional baseball player is Talent and you need alot of it. The great pitchers in High School dominate mainly because of speed on their fastball. The great pitchers in college dominate because of speed + movement and the great pitchers in Professional baseball dominate because of Speed, movement, and location.
The great hitters always have good hand eye coordination and the ability to recognize their zone and the pitch coming at them. The ability to react to a 95 mph fastball, I think you are taking for granted because of how frequently you see it and how often it is hit, but I can say with almost 100% certainty that with 2 years of continued practice that you would not be able to catch up to that pitch. Lets say that you do finally get the hand eye coordination and muscle twitch to hit that pitch regularly, then you have to start to learn how to hit professional sliders, cutters, changeups, splitters, etc. And believe me when I tell you this, all those pitches you see out in the school yard do not at all compare to what you is being thrown at the professional level. Even Low A ball would be a monumental struggle for you.
When I look at professional umpires on TV and compare it to what I do at a much lower level, I think that on TV their job does not look that hard. They work a 4 man system where there is not that much movement, except for fly balls and low liners out to the outfield and rotating for the home plate umpire to the 3rd base bag and the trailing first base umpire for rare calls at home for them. That is about it.
I then come to my senses. I would probably say on average I see fastballs in the 75-85 mph range in HS, 80-88 in Legion, and probably the same for the college summer leagues as Legion. But you have that rare occasion where you get a big left handed pitcher who catches you off guard, like I did 2 summers back. He threw 90-93 consistently with the usual left hand movement. It was a struggle first 2 innings just getting used to the movement on his fastball at that speed. So I could only imagine what a 98 mph fastball is like with even more movement.
What I would say to you star if you really believe you could play pro baseball, give it a shot, it would never hurt. Play in a summer league and get a feel for what it is like to play at a level of competition that you are not used to. See how it goes, if you believe you are better then what you are competing against then try out for a pro team. I am pretty sure there are local scouts who hold tryouts in your area.
Good luck.