We recently moved into an apartment. Before we moved in, the super replaced the carpets and painted all the walls. When we first moved, the smell of paint was quite strong and it caused all sorts of problems such as dizziness, shortness of breath and itchy eyes and nose. Now about a month later, I can still smell paint when I enter the apartment. Although I don't feel as dizzy as before, I still have a bit of trouble breathing. Could it be the chemicals they used when installing the carpets that could be causing problems?
What can I do about this?

Here is a whole search engine on the new carpet sick building syndrome.
AOL Search results for "remedy new carpets sick building syndrome"

The Doctors Book of Home Remedies II Sick Building Syndrome

Apparently the carpets are still outgasing the chemicals. You need to open the windows when you are not home if possible to air out the carpets as much as possible. New carpets are a real pain to deal with until they outgas. It should take about 3 months to completely outgas if the carpet "paint smell" was that strong when you first moved in that you got headaches from it. I am very sensitive to this carpet outgasing so you could say that I know quite a bit about this subject firsthand (unfortunately). Also if you have ceiling fans leave them on when you are not home as well or just a regular table or floor fan will do wonders also.

Thanks, both of you for your answers. Ièm thinking of hiring a professional to test the air. Maybe get a few houseplants and try other easy and affordable things to clean the air.

Yeah spider plants and ferns would be good I would think

Thanks to everyone for your input.
twinkiedooter, should I point the fans towards the open windows?

Do you guys think the landlord will remove the carpet if I ask him? Is it my right to get it removed if I so choose?

You can not remove it. You would have to tell the landlord that it is making you seriously ill.
Maybe tell him you don't want to end up having to sue him for doctors bills.

I talked to the landlord about the carpet. I described to him our problems. He told me that the carpet is called berber and that in the 10 years that he's been a landlord, no one has ever complained about the carpet. Also, I just want to add that the landlord painted our whole apartment and the paint he used is now peeling. Not just on one wall but it's peeling on all the walls. Could this be the cause of any problems? Thanks