Need to is correct. “You need to do your homework”
We use “too” when there is an excessive amount of something or as a synonym of also.
Two verbs in English
When we want to use a second verb in English, we need to use an infinitive(to) or a gerund(ing).
I want to go to the cinema.
You need to bring your passport.
Notice that the first verbs above(want, need) use the infinitive form for the second verb(to go, to bring).
For this reason, we use “need to” and not “need too”.
When to use “Too”
We use “too” when we are uncomfortable with the situation.
I ate too much food.
It is too hot outside.
So, you can see that “need too” is not a common expression in English.