You are correct that child means बच्चा (singular) and children means बच्चे (plural). But it is a little more complicated than that.
To say "you are a child" in Hindi we'd like to say तुम एक बच्चा हो but this is wrong, we have to say तुम एक बच्चे हो because तुम is always plural. This is like why for example we also say तुम छोटे हो (and not छोटा) or तुम लंबे हो (and not लंबा).
In English when referring to just one person we always use the singular form of the noun, unlike Hindi. So we say "you are a child" and never "you are a children".