Passing less after starting T? That's the first I've ever heard of that circumstance. I don't really think you are horrible for letting this bother you, especially since T usually does a good job masculinizing your physical traits with some time. It's reasonable to have those feelings after taking that big step forward towards actively altering your body.
The fact that your job is new explains a lot of things. If you were passing well before to the general public, it's probably because people don't take too long to observe/think about your features or probably judge by your appearance alone with a glance. I'm sure the young kids wouldn't be able to scope you out. However, certain jobs in general, especially yours where you have to handle kids, require plenty of direct and more in-depth social interaction. There are bound to be people out there, particularly adults/parents, who have a keener, experienced eye and ear for scoping out what you biologically were; After all, they've had children to observe while they were growing up.
Drew sounds like a very masculine/boys-only name to me. In my experience, I've never met a female named Drew. I don't think the name would pose to be a major problem, IMO.
My suggestion to you for your voice is to practice speaking in a calm voice at home while adjusting to it. That way you will have time to look for the right balance between gentle/masculine without feeling pressured to come up with it on the spot during your job. Having a good grip on your voice, I imagine, does take some getting used to, since it's equivalent to a teenaged boy going through puberty. Since you're actively taking T, practice would benefit you feeling better about your vocal cords and how your voice sounds. If you have any favorite voice actors or male actors with voices that you admire or want to be like, I would suggest listening to some of their voice clips and trying to imitate their lines, especially if they have kind-sounding ones. It's a good confidence booster.
I think your boss would be the most important person to talk about your gender-identity. After all, once you speak with them and get things cleared up, your co-workers should recognize you as male as well and everything should gradually fall into place. I can understand the fears though, you most likely don't want to lose your newly earned job. Just confront him at a good time in private and ask to speak to him.
I'm sure with more time, you will be passing without needing to deal with any of this hassle. Good luck with everything dude.