What can I do to keep people from thinking something's wrong with me just because I don't get wildly emotional at every little thing?
Buddhism recommends what's "praised by the wise" and being inoffensive.
Perhaps try to be like a good parent or teacher -- or a mature adult, a reasonable human being, perhaps somebody with high "emotional intelligence" or a great deal of courtesy?
I say that because, for example, if you manage young children then things will happen -- they get upset, they hurt themselves, they might hurt each other if you're not careful, they don't self-regulate as much as adults do (self-regulation is a learned skilled).
And their parent or teacher is (I think) meant to be sympathetic and loving (at least they in conventional society that I know) -- and practical, and probably highly moral especially if you're a teacher (and not, "convicted of a serious crime") -- without getting too upset themselves when a child is crying about something.
Specifically-Buddhist doctrine on how to relate with other people seems to be to pratice the brahmaviharas when you're in company. There are several articles about that here. I think it's evident in standard Buddhist interpersonal messages like "may you be well".
If you don't mind my posting it here I admire this lecture (it's not Buddhist) which illustrates various forms of speech and how/when they're proper in different situations.
Possibly you shouldn't "hold your reactions in check", I don't know? But instead express loving-kind reactions. Perhaps a characteristic of well-enlightened people is that they trust themselves to act appropriately, and so they allow themselves to act.
Then again I sometimes read of stories like Is That So?, the guy doesn't seem wildly emotional to say the least, but he seems trusted or respected by his neighbours, and acts appropriately even though he says not much.
I think people appreciate it when there's some two-way communication (I once heard someone define "communicative" as, something like, "receptive" plus "responsive").