Air purifiers

Our breathing/coughing issues with my 22 month old son continue.  Our doctor is hopeful that if/when we have warmer weather that stays, his cough will disappear and his lungs will mature enough over the summer that the cough and breathing trouble won't come back in the fall.  He is now on about the 8th round of steroid just this winter, and as soon as he finishes up the prescription, the cough is back within 2 days.  The majority of his issues are at night and it is very disrupting to his sleep (and ours). At this point, I know we are close to spring weather, so I hate to start switching doctors and getting a second opinion, because I have a feeling our doctor may be right (he was much better the week we were in Florida for Christmas).  On the other hand, I hate giving him so much medicine, especially the steriod stuff over and over and over, and I hate that he is so miserable.  Anyhow if he is having allergy/asthma problems, I'm wondering if an air purifier in his room would help.  There are SO many options out there, and I'm lost.  Does anyone have a good recommendation for a good air purifier?  Honestly, I would prefer a good name brand one, and I don't want to spend a ton, but from my quick research, I know over $150 is a possibility, and I'm ok with that.  I'd rather spend a bit more and get a good one that could also function throught the rest of the house also.  And I see some of them are silent, which isn't necessary because we are hoping to replace his regular fan in his room (for noise) with the air purifier.  Or I suppose a smaller purifier in his room, as well as one in our main living area also.  I don't know, I'm open to suggestions and help!  Thanks!