Welcome to Just ANswer
Has your son had X-Ray's?
Has he been on any antibiotics for infection?
Does he have a cough or any other symptoms?
Was he having breathing troubles before you took him to the hospital?
Does he have a fever?
How long do his lips stay blue?
Turning blue is a condition called cyanosis.
It is sometimes normal for a baby's lips to turn bluish in color after a crying spell, however to just turn color for no reason is not normal. This usually means the baby's oxygen saturation levels are low, being between 85-90%. This is not something to pass off as normal, and does need further evaluation!
In a baby this young, there are some things that should be ruled out. First, a heart defect, however, you said that was ruled out already. Second, a condition that causes breathing difficulties such as asthma, or infection such as pneumonia, or other lung infections. The X-rays he had would have ruled out the pneumonia.
It is also possible that your babies reflux is associated with his cyanosis. Babies that have reflux may cough , or gag, or even temporarily choke on the formula that comes back up. This could also cause his lips to turn blue for a second, due to reduced oxygen levels. Furthermore, sometimes hemoglobin levels that are abnormal can cause cyanosis in a baby. He should also be checked for conditions such as anemia.
I am sure your doctor has probably run most of these tests on him already, however I would advise you to be certain. If nothing can be found, the possibility of it being related to his reflux should be investigated. If your doctor cannot assist you, it would be wise to seek a second opinion. Thank you