Hi matilda, Both are right but they have a slightly different meaning.
At the end of my walk I was very tired. ( means -- at the finish ---- you can`t use in the end here )
I didn`t like English food to start with but in the end I really loved it.
( gives the idea that after time something has changed)
Also --- We searched for ages and in the end we found a hotel with vacancies.
( means --- eventually )
You cant use " at the end " in the last two sentences