What should I do if I overheated my drill motor and made it smoke?
Let it cool down in front of a fan for an hour and try using it again. If it doesn't feel right then you will quickly know.
Have I caused serious harm to the motor?
There's really no way to answer this question without taking it apart and inspecting the motor. The pre-requisite is of course that you know what you're looking for once you've disassembled it.
Is there anything I can do to ameliorate some of that harm?
What's done is done. The main thing is to let it cool down adequately before using it again. If it's warrantied then send it in for repairs.
That drill has a 5 year warranty; I hope you registered it and can make use of the warranty.
So you've learned what that drill's max potential is, now you have to ask yourself whether that potential satisfies your needs. If your needs exceed the drill's capabilities then the realistic question is, which drill should you buy to satisfy your needs?
If the drill is still within the store's return window then I suggest returning it; why move forward with a hobbled drill?