It sounds ok - it's just not a basic Alfredo Sauce recipe.
Your basic Alfredo only consists of:
butter (1/4 cup or so)
heavy cream (about 1 cup)
crushed garlic (1 clove should do it unless very small)
Parmesan cheese (about 1 1/2 cups grated will do - reserving some for sprinkling when done)
salt and pepper to taste
Note that the cheese will add saltiness so don't use too much salt in the beginning. Wait until after the cheese is added and then add from there.
Melt the butter, add the cream and reduce (do not let boil) - heat at medium-low. Once this reduces for maybe 10 minutes or so add most of the cheese and cook until melted more. Toss in your drained fettuccine and already cooked chicken chunks. Cook the chicken chunks with a bit of oil, garlic, and even some lemon squeezed on is good.
There are recipes that use egg yolk but this is a good one to get you started IMHO.
"Count yourself...you ain't so many" - quote from Buck's Daddy