私の答えはあなたの質問にあってますか？って英語でなんて言うの？

Native speakers will say like this: “Does this anwser your question?”.
There are lots of other ways to say it, but this one is the most accurate and most commonly used.
Here is an example on how to use this in a conversation:
A: ... does this anwser your question?
B: It does, and it's correct.

Did my answer make sense?' - This is asking the teacher whether the words you said were put into a sentence which allowed her to understand what you were trying to say. She would either say 'Yes' or 'No, I do not understand what you are trying to say.'

'Did I answer your question?' - This is asking the teaching whether the answer you gave her was fitting to the question she asked. She would either say 'Yes.' or she would repeat the question in a different way so that you could understand the question.

If you want to check if your teacher understood you, you can use the above sentences.

make sense - easy to understand; clear meaning

If you want to check if you understood or answered the teacher's question correctly, you can say the following:
Did I understand your question right?
Did I understand your question correctly?
Did I answer your question correctly?

When we are asked something but are not clear about the question it is a good idea to check with the person to see if the answer was adequate.

These are great phrases for those still working on comprehension. It's a simple way of checking with those you talk to if you are understanding and communicating clearly. Such questions can reduce the confusion that happens when two people are talking about two different things in the same conversation.