"I am not looking for you."
If "you" is not stressed, use the short form "tě" (second position):
- Nehledám tě.
- Já tě nehledám.
If you want to stress "you" (It is you I'm looking for), place it last:
- Nehledám tebe.
- Já nehledám tebe.
Your version "Já tebe nehledám" is not wrong, but be aware that it stresses everything - it's a very tense sentence. It stresses "já" by including it in the sentence, it stresses "tebe" by using the long form instead of "tě", and it stresses the negation on "nehledám" by placing the verb last. All this stress makes it sound rather angry.