I am sorry to hear that you are so miserable. It sounds like you may have two things going on: 1) an upper respiratory infection or allergic reaction to something you were exposed to in cleaning your house and 2) an upper gastrointestinal disorder, responsible for the vomiting. It Is also possible that your vomiting may be due, at least in part to excessive amounts of swallowed phlegm.
What is clear that, whether one or the other of the preceding problems persists, you do need to see your doctor because, “the very stuffy nose and very itchy throat” may reflect a treatable infection that might also be effecting your lungs (bronchitis or pneumonia) or, if allergic may respond to a short course of prednisone and, if the vomiting persists, you may soon become dehydrated. In response to your question, I would favor your seeing the ENT, who could also assess both your upper and lower respiratory tracts, with physical examination, a chest X-ray, a blood count and, especially if the phlegm is discolored, examination of the phlegm being raised.
Good luck, I sincerely hope that you are already feeling better.
Thanks a lot for the information... It was a great help. I was diagnosed with Acute Tonsillopharyngitis.