Referring you for a PET scan doesn't automatically mean that you have cancer. However, PET scan is extensively used in cancer patients.
A PET scan is a functional and anatomic fusion imaging which detects areas of high glucose
uptake in the body.
From the details you provided, it seem your mum has either a lung nodule ( 3 cm).
If its only one in number, its a solitary pulmonary nodule
/ mass (SPN). SPN can be due to cancer or be due to non-cancerous conditions.
The simple dictum is patients need a biopsy
or excision if the suspected lesion is active on PET scan. The patient can be safely followed by if PET scan is negative. Obviously, there are exceptions to the general rule.
In my opinion, your mum should have been referred to a PET scan to find if the suspected area is active (glucose utilisation is high) or not.