The pattern of symptom development you describe (onset after moving in, resolution after an extended vacation) are strongly indicative that the health problems you are experiencing are due to some type of exposure in your house. Indeed your house may be making you sick.

Old houses, particularly old houses with basements are at high risk of having been or being infested with mold. Mold infestation may occur on materials stored in the basement, on flooring joists, in the walls under windows, etc. There are a large variety of mold species that are known to cause allergic-type symptoms as well as sinusitis. The mold-type you are exposed to may be a significant factor in diagnosing the nature of your problem. The mushroomy odor suggests that the mold infestation is at least in part due to wood-decay fungi called basidiomycetes. Though known to cause allergy-type symptoms basidiomycetes species are generally not present in standard mold mixtures used by allergists to test a patient's sensitivity to mold. As a consequence, allergy test results may indicate that you are not sensitive to mold. Since these tests do not include basidiomycetes mold allergy cannot be ruled out.

Lightheadedness and a tendency toward nausea can be caused by a number of different exposures, including carbon monoxide. They can also be associated with sinus infections that are often difficult to confirm clinically.

In this particular case you can consider a variety of options. You may wish to have your home tested for airborne mold to determine mold types present and their relative abundance. Most consultants who conduct indoor air quality investigations use a sampling technique that collects airborne mold on culture plates and then allow it to grow for identification and enumeration. Basidiomycetes generally grow poorly if not at all on such media. As such, test results may be misleading. As a general rule if obvious mold infestation is present you have a mold problem, no matter what the air test results indicate.

Since you do not own the home you are residing in your options are quite limited. It is often very difficult to convince a landlord to fix a problem which may prove relatively costly or who does not perceive it to be a problem. In the short term you may choose to live with the problem. In the long term you should seriously consider finding another house or apartment to live in. Inspect it first for obvious mold growth and/or odor.