I think you are on the right track here. Mold is very common in older apartment buildings, and it is one of the most common causes of 'inside allergies.' It is entirely possible for your girlfriend not to have any symptoms, especially if she is not allergic to mold but you are.
Symptoms of inside allergies include congestion of the nose, sneezing, and copious nasal drainage. Some people will also have eye allergies at the same time, characterized by redness and itching of the eyes. If you have these symptoms, you should definitely go see your primary care doctor
because there are effective medications that can be used to treat inside allergies.
For example, non sedating anti histamines like loratidine (Claritin) and cetirizine (Zyrtec) can be extremely effective. For more prominent nose symptoms, nasal steroid sprays like mometasone (Nasonex) and fluticasone (Flonase) are very helpful.
It is also sometimes necessary to modify your living environment. For example, if you have a lot of carpet that might be the source of the mold, and you might be able to take the carpet out and mostly eliminate the problem.
Start by talking to your primary care doctor who will have additional advice for you.