Hi, runny nose and itching may be due to infection or allergy. Non-infectious causes of itching are Chemical or other irritant, Allergic, hypersensitivity, and dermatitis. If runny nose stops after coming home then it may be due to allergen.
Also it may be due to acute sinusitis. There may be draining sinus which has been source of infection and causing persistent runny nose and headache.
The nasal secretion (or endoscopic guided) for culture and sensitivity should be done. Analgesics, nasal saline irrigation, and topical and systemic decongestants can be given for acute condition.
But main plan of treatment is use of appropriate antibiotics against prescription with or without glucocorticoids. You need to identify the allergen and avoid further exposure. Allergen test can be useful.
I suggest her to consult ENT surgeon. Take care and regards.
There might be mold behind the walls or another area that cannot be seen.
There are instuments available that measure humidity levels present, inside walls. That would be a sign for mold. Look into this.
Other possibilities may be emissions from toxic and offensive materials in the house.
Perhaps from the flooring or carpets or wall paint etc. Have all that checked.
Temporary solution get a good air purifier with a HEPA filter. Use a "Lampe Berger"
that cleans the air, kills bacteria and deodorizes all in one action! Very cheap solution.
And ensure that there's fresh air in the house daily!
Use a dehumidifier in the basement.
Hope this helps.
Blessings
Nikodicreta