Ill try and give the best description of this problem but ill first tell you a little info. I drive a 06 Toyota Corolla CE, Its Auto with 140k miles. I take decent care of it and don't go cheap on parts and maintenance. I have done some basic mods such as AEM Short Ram Intake, DC Headers, and Custom Cat-back, Which I deleted the resonator. The only major problem my car has had was a bad water pump and CV axle (Around 125k miles). I keep getting a p0420 and every other week I would get a p0741. Im aware of the p0420 but no clue on the other. I drive my car pretty hard too so that doesn't help.

Now to my problems... First when shifting from 1st into 2nd its rough regardless of speed (Its a automatic). Ive noticed sometimes on the lower rpm's when in 2nd it would rumble as if I went over 1000 little skittle size bumps for about 1-2 secs. Although this could be suspension related or just the roads. Also just the past few days im hearing a "thumping" sound when I accelerate. Kinda like a flat spot on my tires, Although they are new and had them replaced 2 times. I does this noise about 3 times a second and ONLY when I speed up. If I remove my foot from the gas, idle, Or just it into P or N its fine.