You can be aggressive in any and all of them. Judo, Brazilian Jiujitsu, wrestling, boxing, kickboxing, Sambo, Taekwondo, different types of karate competitions, you name it. What's available in your area? What appeals to you, personally, the most?
The sports is not aggressive, the fighters are. So you can pick anything you want. If a fighter is not aggressive in any fighting sport he is not likely to win. This thing about 'fighting defensively' is a myth and comes from a school who does not know how to fight.
Wrestling or Brazilian Jiu-Jitsu
Muay thai, Judo guro, and Okinawan Karate and Kajukenbo.
wrestling, judo, boxing, kickboxing, muay thai, kino mutai.
And allows you to compete? MMA is off-limits, unfortunatley.