2001 Impala rough idle-shaking

My 01 Impala 3.8L takes more than 5 minutes in the morning for the idle to go down and when in drive it shakes and makes more noise than usual. Also,
when accelerating while going 10 mph the car started to shake and felt like I had run over an animal. The car has only 30K miles. What could cause this? If I go to the dealership they will charge $150 to diagnose since no fault codes are present. I am assuming if the engine light is "on" a fault will be stored. Thank you for any suggestions.
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No matter what it has to be scanned, especially when the problem happens,. could be a coolant temp sensor sataying in the cold mode, this will not set a code, this is the starting point only.

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