when does the coughing stop?

Okay, I quit cold turkey exactly 100 days ago after smoking for 55 years.

I had just retired and realized that there was no way that I could afford my 3 pack a day habit living on my retirement income.

Doing good except for this cough I developed the day I quit smoking. I never coughed the whole 55 years I smoked but now I cough up this grey mucus several times every day. Is this normal? Is this my lungs trying to get rid of 55 years of tar?

Any knowledge or experience would be appreciated.