This could perhaps be interpreted in two ways: "I too have needs" - "I, as well as everybody else, have needs" and "I have needs too"-"I have needs, along with other things which I already have", the two meanings depending on the position of that tricky little word "too". Can you move "też" around to the same effect?
I'd say "(Ja) mam też potrzeby" for "I have needs too", although "I have needs too" is currently accepted.
One observation: the more I write in English, the more such mistakes I make ;) Usually I see them immediately, but clearly not always...
For example, 30 minutes ago I wrote "wan" instead of "one".