Go to an Allergist specialist and get tested.
As you are not getting any relief from antibiotics or allergy medicins, it is likely that you have a virus and chronic (long lasting) sinus problems.
I have a similar problem. I was prescribed with a nasal spray the other day to help dry up the post nasal drip that causes a wet cough.
Antibiotics will not have any effect on viral infections.
You can try steam inhalations. A hot bowl of water with Vick or Olbas Oil if you wish, put your head over the bowl and cover it with a towel and breathe in and out. Take care not to scald yourself. This will help to loosen up the blockage.
Take care with long term use of nasal sprays because although short term they can help, long term they can make the problem worse (so the instructions on the leaflet say).
As a last resort your doctor may recommend that you have your sinuses washed out by referring you to an ENT specialist.
Best wishes
Sounds like allergies could be problem. I also take antihistamines and when I get a flare up a doctor told me to get a Medipot or the container and use to rinse out my sinus's. You can only do it twice a day at the most and usually I only need once every day for a while. Make sure to use distilled, not tap water and heat water to lukewarm, add the salt and lean over sink as instructed. Most allergists have people use these now and they help.. good luck!