The Local Government Association (LGA) said doctors could play a role in educating people to treat their own minor conditions, estimating the reduction in "unnecessary" appointments could free up an hour of a GP's time.
The body, which represents 370 councils in England and Wales, cited figures suggesting one in five appointments is for back pain, headaches and colds, costing the NHS an estimated Â£2 billion a year.
In March 2015, data from the Proprietary Association of Great Britain (PAGB), the UK trade association for manufacturers of over-the-counter medicines and food supplements, showed 19.1% of visits (3.6 million) to A&E are for minor issues, while GPs preside over more than 57 million consultations a year for minor ailments such as back pain or flu.
The LGA said councils, which have a responsibility for public health, have been behind a drive to improve "health literacy" among patients.
Coun Izzi Seccombe, chairman of the LGA's Community Wellbeing Board, said: "We need a new culture of care, where people stop and think before calling the doctor.
"GPs and A&E departments are already overstretched. However, many appointments are unnecessary and for minor conditions that a person could treat or manage themselves.
"But patients need to be helped in learning how to look after themselves, for example in managing long-term conditions such as heart disease or diabetes, and GPs can play a key role in this.
"Many patients want to be more involved in their care, as it gives them a greater sense of control and improves their quality of life. Better self-management could make a huge difference to a person's physical and mental wellbeing.
"Instead, the lack of knowledge among the general population about how they can do this is placing a huge burden on surgeries and hospitals."
Professor Ian Banks, Self Care Forum Trustee and former A&E doctor, said patients needed support to be confident enough to care for themselves.
He added: "Self care is not no care. Far from it, for example you will find the local pharmacist an excellent source of health advice and information. There are also reputable health information websites such as NHS Choices or the Self Care Forum website."