1997 Cadillac Deville car shakes when first turned on

Other Category problem
1997 Cadillac Deville V8 Wheel Drive Type unknown Automatic 108000 miles

Hi, I have been having problems with my car for weeks. I constantly have to add oil to my engine (like every 2 weeks, about 2 quarts) and I recently had to change my coils because my check engine light came on and when the car is started it shakes. Well the car still shakes when it is turned on and it shakes a little when turning to the right. My mechanic said when my water pump was replaced a clip was not used and there may be damage to my head gasket. He says this is a very costly job, I just paid him $700 to fix my coils and to do a tune up, 2 months ago paid him $400 for the water pump to be changed. Do you think this shaking on the start could be caused by the head gasket and is it really an expensive job to do? Also on an older engine is this job worth it? Also I have not seen any overheating warnings or lights other than that check engine light prior to the coils being changed.

THANKS In Advance