今日はテストだけ？それとも授業もありますか？って英語でなんて言うの？

This is a direct way of asking a teacher or someone else if the test/exam is the only thing you are doing at school that day, or if you also have your normal classroom lessons too.

There are a variety of ways that you can ask this question. Each of these should give you the answer you are looking for:

-Do we have normal classes after the test?
-Are we just doing the test today or normal classes too?
-Can we go home after the test?

"Do we have classes after the test?" is a short question where as "Is today's lesson only a test or do we have class after as well?" is slightly more elaborate.

If you ask "Are we only the doing the test today?", it is an indirect way to have your teacher tell you whether there will be a normal class afterward or not.
"Will there be a lesson after the test?" Is a more direct way of asking your teacher if you should expect a normal lesson after the test.

テストの後に家に帰ることはできますか？
Can we go home after the test?

テストの後にクラスはありますか？
Do we have classes after the test?

There are several ways in which you could ask this question. 'Do we only have a test today?' is asking if there is anything else to be expected. 'Do we have lessons today?' is specifically asking if there are going to be lessons. 'Do we have anything except the test today?' is asking the same question using the more advanced word of 'except'.