2002 Nissan Altima second opinion

I recently took my 2002 Nissan Altima into the dealership because when I started the car it chugged for about 30 seconds before it would start to run normally and the check engine light came on. They checked it out and said it was the cat converter and the head gasket for $2700 or probably the engine was damaged because these two were bad and that cost $4700. The background on this car is that I bought it new, have brought it in to the same dealership for the past 5 years, had a 90,000 checkup a month ago and have always be faithful about oil changes. I've been in 14 times in the last 5 years. The check engine light has come on two times and I brought it in right away both times. I've had coolant problems. First they said I had a bubble and just added more and once they replaced the cap. I guess my question is what caused the engine damage and are they right that it needs a whole new one. Why didn't they catch anything the 14 times I've been in. How can a cat converter cause damage when I think it is on the opposite end of the car. I'm a women and not very mechanical. Hope you can give me some insight into why this wasn't caught and explain if they are right or giving me a line. I am sincerely appreciative if you have any suggestions. Janice