What you describe suggests that this child has a chronic respiratory condition. It is most likely asthma, but there are a number of chronic respiratory conditions that could present this way. The severity of his symptoms suggests also that this disease poses a threat to his well-being and could conceivably be life-threatening. In any event, this is definitely not a "common cold.", and almost certainly warrants medical evaluation and treatment. Most states provide and may require a course of action to be taken in the circumstance you describe, which sounds like medical neglect. In many, if not most, states, you are required to report your concerns.
In Colorado, the program is conducted through county departments of human services. In other states it could be through the state department of human services.
You might begin by speaking with another responsible family member, perhaps the child's father or grandmother. If that is not an option and if you are unable to persuade the mother of the necessity to get medical care for her son, you may want to take the child to a children's hospital or similar emergency and/or report your concern to human services. Should you take the child to an emergency and explain the situation, they will almost certainly contact human services.
I am so sorry that this little guy is having a hard time. can you leaglly take him to the doctors. I think you would be protected if it was an emergency, I would hate to see you get into legal issues for taking him without consent.
I think you should go with your gut feeling. if he is that bad then he definately should be seen sooner then later, in my opinion. is he turning color at all around his lips/mouth or his anil beds, if so he needs to be seen immediatly. this is a sign of low oxygen going through his blood to his brain.
I am not a doctor, just a mom with a child who has had many many times of having difficulty with breathing. I think this mom needs a wake up call. I was only 20 when I had my first one, but if someone told me something was not right with him, I would be at that doctor with in a few days
good luck and I hope this little bugger can get seen.
Michelle