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[Alpha Six]

Trish is a really weird rushdown character, you'll require a lot of practicing with her to figure out her rushdown game. Her keepaway game is really easy to learn, especially with her traps.
If you want solid rushdown, try X-23; she's the fastest character in the game, and she can use her Mirage Feint + Talon Attacks to really confuse the opponent.
Wesker is also a good choice, since he has major damage output, average health, a fullscreen super and a counter super.
I'd also look into characters like Spider-Man, Wolverine, and if you feel like putting in the learning effort, C. Viper can be a good choice. Also look into using Akuma (everybody is good with Akuma), and if you're a risk-taker, pick up Phoenix, since she is incredibly versatile as a rushdown, keepaway, and mix-up character.
Although really, any character with a teleport would make a good rushdown character, with the exception of Dormammu, and they double as mix-up characters, since properly used teleports can confuse.

With Ammy, do you take advantage of all of her weapons? Most Ammy players I see only use the Reflector, which at this point has become predictable.

Also, be wary about consistently offensive rushdown, as it becomes very predictable and very punishable, very fast. Use strategic rushdown-- figure out your opponent's movements and then come up with ways to counter them. You want to reel them in first and learn their patterns so you can exploit holes in their offense/defense. And if someone is consistently on the defense, teleport characters (Wesker, Phoenix, Deadpool, Akuma, to an extent X-23, etc) are your biggest tool.