Can houseplants actually improve air quality?
I would do both plants and an air filter.  You can purchase a reasonable sized air filter for $89 on Amazon (Honeywell 17000-S QuietCare True HEPA Air Purifier, 200 sq ft) that does a pretty good job of helping clear up the air.  https://www.amazon.com/gp/product/B000050AQ5/ref=oh_aui_detailpage_o02_s01?ie=UTF8&amp;psc=1  I use this one because it's large enough to make a noticeable difference, but small enough to not be obtrusive, which you would probably want in an apartment of this size.  I have one in my den, another in my LR, and a third larger one in my BR, but I have a dust allergy (you may want to get tested for allergies...Dust, mold &amp; pollen allergies can cause headaches).  It's relatively quiet as air filters go.  I've tried smaller and larger models, which were respectively ineffective and too loud and too visibly large.  I've also tried a model with an ionizer and permanent filter, which had a horrible smell, and ionizers are irritating to the lungs.

I also have about a dozen smaller plants, and they refresh the air in the immediate vicinity, but they would not be enough by themselves. To help the plants and increase the freshness, I also bought a water based air purifier humidifier by New Comfort ($45 on Amazon), which I place near the plants in the dry months, and this also helps me breathe better.  

Finally, there is the issue of what is causing this air?  It could be the laminated floor still offgasing formaldehyde (the issue is complicated - see http://inspectapedia.com/indoor_air_quality/Formaldehyde_in_Laminate_Flooring.php). If you bought any new furniture, it could be from that if it contains MDF, which most does.  Sealing the MDF may help. It is difficult and expensive to accurately determine your air quality and what may be causing the problem. 

It could be dust - in the fall, when the heat is first turned on, the air becomes particularly dusty and s/w smelly if you're sensitive to that, but then it levels out.  I'm in a private home, so it's easy to check the furnace air filter, but if it continues you may want to do that or ask the sup to check it - a dirty filter and/or ducts can cause what you describe, too. Frequent vacuuming (with a HEPA filter) may help, as may installing dust filters over your heat vents.

To prioritize, I would start with an air purifier such as the Honeywell 17000-S, and see if this helps, then proceed with other remedies.  Good luck!