Sounds like you have some work to do but hey if you are up for the challenge than thats a great start. Im 18 years old in my last year of high school i know how u feel man. one thing have patience and work with a purpose and a goal everytime you work.
-To get that arm stronger playing long toss will definetely help.Some may say 5 times a week is too much, but it really depends on the arm. If you cant go five times a week, then work on staggering your days like a monday wednesday friday thing. I dont too much about the bullpen situation, I play MIF.
-Leg exercises are good. Squats, Leg Curls, Jump Squats, calf raises, leg press. four times a week i dont agree with because you need to give them rest
-upper body. Not a focus in my workout, not needed for baseball. But I was speaking to my workout partner about it and we still do it with dumbells,instead of the barbell, just to have an overall fit body ya know. pullups and dead lifts are for the back. so three times a week is not good.
-Throwers ten is good and band workout are also good. incorporate both.
-The running is good because you want to work on your speed and have endurance since your a pitcher so that mile is nice. Get a good strecth! Before you run you might want to start off with a dynamic warm-up.
-core exercises everyday not good. you have to give them a rest. atleast two days.
-Back exercise are good, the deadlifts and pullups are good.
Also you might want to get cleans into the program.
Look up some workouts from others on this site. you can find some under this tab (strenght and conditioning). Hopefully this helps. Im not a trainer but I know a few little things. Also what helps is mixing up your program, not always doing the same workout for each day the whole summer.if you have any questions I would be glad to answer. HOPE THIS HELPS!