"I am not going to school today."
Translation:Nie idę dziś do szkoły.
Well, firstly the sentence was that you're not going to school, and you wrote one saying that you are going.
Secondly... well, it's not that no one will ever use your word order, but it's rather surprising. If you talk about "today", than it's hardly a new piece of information. The new, most important information seems to be that you're not going to school. For which you'd either use "Nie idę dziś do szkoły" or "Dziś nie idę do szkoły".
Well, the hints system is surely imperfect, and the fact that it favors multi-part hints is sometimes problematic. Also, this hint comes from the English for Polish course, which teaches it to use Future Tense in English.
"nie zamierzam" translates more literally to "I do not intend". It's the "going to" as in "I am going to throw a party on Saturday" or "They're going to cook dinner tomorrow". Nothing to do with actual movement, it's just accidentally the same phrase in English.