2008 Accord shakin at ALL speeds
 

Hi,
I have a 2008 Accord LX-P with 51k miles. Bought it last year in MAy with 38k miles. I didn't put a cent into any repairs since than. Only changed oil.
About a month ago I changed front breakes myself. I don't think it has anything to do with the shaking, though. Around that time the car started vibrating/shaking when accelerating from a stop. As soon as I start to drive it happens. It was not very noticeable at first, but got noticeably worse in the last week. It only happens when accelerating. When I take the foot off the gas pedal it goes away. When I break it goes away. In neutral goeas away. In stop in neutral or in parking it goea away. The car drives straight and does not pull to the side. The tires wear evenly.
I left it at a shop today. The mechanic couldn't find the problem so far. He lifted the car and had somebody accelerate in gear and the problem does not replicate, so he thinks it is in the drive system somewhere. But he cannot locate it. He says everything looks good and he will continue to look tomorrow.
Anyone has any ideas on what it can be?
I bought four Michelin used tires (a set) last December with very good thread and they were performing well so far. The wheels were balanced at the time. Is it possible one is going bad? I rotated them last week but it didn't help. There is no noticeable bulging on the outside sides, but maybe hidden? I asked him to check it tomorrow.
Is there anything else you can think of that may be contributing to these symptoms?
Any input will be greatfully appreciated.
Thank you up front.
P.S. I checked the transmission fluid and was very low. I added a full bottle and now is at good level. I think it improved the shaking a little, but I might be self-suggested on this one since I know I know I did something. The problem is still there.