Hi S.,
Flem is the body's natural reaction to protect the nose and nasal passages, etc. from irritants like bacteria, fungi, and synthetic chemicals. If nobody else in the home is sick or if his is just lingering on, then you probably have some chemical issues in your home. Most of us do but they affect different people different ways and a 6 week old is going to be hypersensitive to it.
I detoxed our home and removed all the synthetic chemicals and all our allergies and colds are gone. These chemicals, laundry detergent (even Dreft), baby products (Johnson and Johnson are the worst in my opinion), even the soap you use on yourself that he snuggles up to can be dangerous. These chemicals contraindicate just like meds do and we don't know what combination we are exposing ourselves to. The breastcancerfund.org did research and in their summary of the paper State of the Evidence documented that an average of 44 toxic chemicals pass through the umbilical cord in utero. I have read other documents that have stated higher but I can't remember them off the top of my head.
Detoxing can be simple and inexpensive and will help everyone's health in the home. Removing carcinogens is always a good idea :)
This may not be the only irritant for your little guy but removing these types of irritants will strengthen his immune system so he'll have a fighting change against the other things and can fight off what ever this is.
If you'd like help or would like me to walk you through the process, let me know. Hope I helped!
Regards,
M.