NHS England says there are 18 million GP appointments and 2.1 million visits to A&E for self-treatable conditions every year, costing the NHS £850m.
However, millions of parents could save time and receive expert advice by taking their concerns to their local pharmacist first.
The drive is part of the Stay Well Pharmacy campaign, which also features TV, digital and social media advertising.
NHS England says research has shown only 6% of parents with children under five would consider seeking help about a minor health concern from a high street pharmacist as the first port of call.
Dr Ellie Cannon, health columnist and GP, told Sky News: "I think it's a fabulous idea. Pharmacists are not shopkeepers, they are healthcare professionals.
"The British public and parents must remember that they have trained for five years and their knowledge of minor ailments is excellent."
She says it is also a great way of relieving the pressures on general practice and the NHS.
"The other beauty of pharmacists is they have very good community knowledge - they understand the ailments and health problems affecting a community. For example, they will be aware of vomiting viruses going around," she added.
An overwhelming majority of adults (79%) say they are aware that pharmacists are qualified healthcare professionals who can give advice on most common illnesses, but parents are still reluctant to go to them first.
Dr Tom Nutt, chief executive at Meningitis Now, has raised concerns over the potential to miss a vital, early diagnosis.
"Whilst we welcome this NHS initiative to better use the underutilised value that community pharmacists offer in treating minor illnesses, we have real concerns about putting another step in the process of swift diagnosis for something like meningitis, which could result in valuable time lost - a commodity which is in short supply when trying to prevent the worst patient outcomes," he said.
Allaying fears that parents might miss something more serious by going to the pharmacist instead of the GP, Dr Ellie says: "A pharmacist is very well equipped to say you need to go the GP so I think it is absolutely safe and quick to start with a pharmacist."