My 3 year old son have a running nose since Labor Day

In the Labor Day,we went to Florida beach and came back with my 3 year old son got running nose everyday since then. I brought him to see the pediatric doctors and allergy doctors. They first said it may be a cold. Then I said it lasted for months. They said maybe he developed an allergy to something. They gave him "ZYRTEC" and "NASONEX" nosal spray. These all didn't help. He still got running nose every minute. His dripping looks clear. He doesn't have other allery symptom such as watery/itch eyes or sneezing like me. Since I got allergy to ragweeds. So since Labor Day, my allergy developed at same time as my son. But my allergy end on October. My son's running nose seems last forever. The allergy doctor said he is too young to do a skin test.(Is that true?)  So I have no clue what he allery to. I went to internet to search some allergens in fall to winter. It looks like the molds and medew exist this time and will go away in the spring time. Please give me some suggestion. His running nose seems to dicrease his appetise a little. Otherwise he plays and sleeps well. It just makes him and us uncomfortable to clean his nose every other minutes.
  My another question is about my 10 year old son. He continutes dry cough evey year from middle of Nov. to Feburary. He develop cough from First Grade until now. He doesn't wheeze. His cough gets worse in the morning. Sometimes he can't eat his breakfast. Two times the doctor let him to have x-ray and found his infection in the nose and give him antibotic (antibiotic) medcine. It seems help. Dose he got a sinusitis or asthma or just flu?

[National Jewish]

Your 3-year-old son

[ozark]

your 10yr old probably has a sinusitis. sometimes it needs to be treated for 3 weks with antibiotics....as to your 3yr old, he may also have sinusitis ...his nose may be blocked higher up and he just drips from his nose ...is his eyes or face puffy? i would inquire about sinus xrays on him too.....my daughter had the night time cough for a while and the dr didnt think she had sinusitis...i insisted on xrays and she did have a sinus infection...was treated and the cough finally went away!  good luck