01 Lumina Shifting wierd

Hello nice forum first off, but have a problem with a lumina i have well heres the problem with it The first 10 miles or so the thing runs great but after that 10 miles the thing wants to shift real funny basically what happens is ill do a fast acceleration and it will rev up and when it shifts to the next gear up, the steering wheel shakes real bad thats where i feel it the most and it then shifts into gear. The harder the acceleration the worse the shaking so if i granny the car it runs ok and shifts ok but i will still feel a slight vibration in the wheel and it doesn't do it in the morning... only after driving it around a little bit

Oh yea and there is no check engine light and also sometimes when i start it it will die right away or sound funny when it starts then kicks in and starts up...