I planned on bringing my own equipment... to be clear... i cannot wear anything identifying me as an EMT? Not even a t-shirt? Because i need to be identifiable to coaches and players.
I can't answer this because I'm not in your AHJ writing your specific protocols, or the by-laws for your company, or so on.
I personally would not wear anything identifying me as an EMT if I was working unofficially in a medical setting because doing so creates the duty to act up to your level of training. It's like the old question of throwing a job shirt on when you go into the gas station. If you don't throw it on, and someone DFOs, you can leave, or not leave, or just call 911, or whatever. You're a bystander. If you do throw it on, and someone DFOs, you're a first responder, you have a duty to act, and if you decide to slink out the back door you're potentially liable.
So if you're at the game, and you identify as an EMT, you need to act as an EMT. And if you're acting as an EMT, you're bound by protocols. That means you lose a lot of options (as mentioned above) and also you're operating on your MD's license.
As for giving meds out to kids at games, I wouldn't see that as my position as an event first responder. I'll dress wounds and that's about it, because I'm not going to assume the liability of asking children what meds they've taken and knowing what interacts with what, even though I have a better knowledge of that stuff than a lot of CFR/EMRs and EMTs and so on due to working in pharmacy for 7 years. I ain't about to roll the dice on that. And I'm not gonna show up with a pharmacy anyways.
Basically I'd look at your protocols for Certified First Responders in your area and not do anything other than that. That way if you did get pressed on it, you could say truthfully that you acted up to your level of training with the equipment on hand. Then again, that makes it seem like you're acting in an official capacity, and that's the major distinction. If you're acting in any official capacity (and wearing a badge or patch indicates you are) then you're obligated to act according to your protocols, and under your MD's direction. If you're not acting in an official capacity, do whatever you feel comfortable doing.
Realistically, nobody is likely to sue you because you didn't put a bandaid on right or you gave their kid 200mg of ibuprofen for a bruise, but then, do you want to risk your certification because you gave a kid a trivial dose of something?