1999 Honda Civic Engine gasping especially after a cold night

Hi, My car engines gasps when I start my engine especially after a cold night or rainy night. This happens even after I keep my engine running for few minutes before I take the car out.

When this happens my check engine ligh goes on/off and all this happens for couple of miles and It seems as if my engine is working at 30% capacity and not moving forward quickly, than evertying becomes normal afre 1-2 miles, and check engine also dissapears when I restart the car next time.

Recently when I driving in a heavy rain this started happening again and engine was not moving the car and I had to pull over and wait until the rain subsided.

Does this mean my engine has aged out and needs a replacement if so can you suggest if I should go with rebuilt or remanufactured engine.

Really appreciate your help.

Thx.