You are definitely NOT wrong. A meter and testing is our best tool to combat this disease, providing you learn from what you see. Your mum is the one that is wrong. It is not why the doctor won't give you a meter. He won't give you one because of the financial restraints in the NHS. Doctors won't tell you that of course, they have a variety of excuses. You are the one living with this disease, so it is your choice, and yours alone.
Carry on testing your meals before and 2 hours after first bite, keep a food diary and record your levels alongside the food eaten. You can learn from this. The aim is to keep the rise from before to after as low as possible, and definitely no more than 2mmol/l - preferably a lot less.