The right answer should be: tomorrow we will pray at the western wall
The only difference I see with your answer is that you haven't capitalised "Western Wall", and as a place name it should be capitalised. However, Duolingo doesn't care about upper and lower case when it marks answers anyway.
Can you also just say בכותל?
Machar nitpalel be'kotel ha-ma'aravi.
Do you use כֹּ֫תֶל exclusively for the Western wall, because usually a wall is called חוֹמָה?
Usually a wall is called קיר Kir.
You're right that Kotel כותל is used exclusively for the Western Wall.
Choma has a different meaning - a large (or long) dividing wall used for bordering and protection against hostile nations...