Barton Barton & Plotkin | Maurice Ross
This question cannot be answered without knowing a lot more information. You need to educate yourself on many legal and business concepts, including the basics of trademark and copyright law. Usually a good idea cannot be protected by ip laws. Further, trademark protection arises out of use in commerce. You might be able to copyright your design for the t shirt and trademark your logo, but before doing so and before attempting a deal with a big company you need to retain and work with ip counsel.
Answer Applies to: New York