At my age I have had enough illnesses to have a pretty good idea which are viral and which have progressed to a bacterial infection.
Gosh, you're terribly clever. I have been to medical school, worked as a doctor in A&E, intensive care and general practice, have a special interest in infectious diseases and I can't tell. Do tell me your secret.
The truth is that there is no way of knowing with certainty which illnesses are viral and which bacterial in a GP surgery (except for things like cold sores that only have one cause). Even if GPs did throat swabs or blood cultures every single time, you'd have to wait 3 days for the results, by which time many people would have recovered.
So a GP's decision whether to prescribe antibiotics is based on:
- probability of it being a bacterial illness
- likely risk vs benefit of prescribing - a patient with an underlying medical problem such as asthma is at more risk of serious harm from a chest infection so the threshold for prescribing will be lower.
A cough accompanied by a runny nose, sore throat etc is 99% likely to be viral. Some people will develop a bacterial infection on top though, which is why antibiotics may have a role if what starts out as a normal cold starts to get worse.
In terms of risk of prescribing, lots of people are harmed by antibiotics every year, in addition to the risk of antibiotic resistance. The harmful effects of antibiotics can be extremely serious, even fatal - including anaphylaxis and clostridium difficile infection (caused by the body's "friendly bacteria" being killed by the antibiotic).
So, OP, YANBU at being fed up of having a miserable cold. But your GP is also NBU at not wanting to prescribe if s/he thinks your illness is viral. She would be putting you and your children at risk of serious harm for no benefit if she prescribed antibiotics for an illness that is almost certainly viral.