Doctors in NHS Lanarkshire said people had been turning up with with ailments which would be better treated elsewhere, including insect bites, sore feet, earache and chronic back pain.
A&E is only for life-threatening emergencies, they said, asking people to use other services such as calling 111 or using the NHS Inform website.
Visits to A&E have risen to pre-pandemic levels in recent weeks. Last week saw the worst performance on waiting times since December.
Staff have also faced abusive behaviour from patients failing to comply with Covid-19 restrictions.
Health boards across Scotland have warned of services under very heavy demand, exacerbated by high numbers of staff self-isolating.
GPs have also warned they are struggling under increased workloads in the community, meaning some patients may make an unnecessary visit to A&E when faced with long waiting times.
Calvin Lightbody, A&E consultant at University Hospital Hairmyres, said: “Over the last few weeks, our A&E departments have been as busy as any time I can remember in recent years, with numbers extremely high for a sustained period. We had nearly 700 patients in a single day last week across the three hospitals.
“We are seeing a number of seriously ill and critically ill patients with urgent issues such as chest pain, strokes and serious bleeding. However, we are also seeing a number of conditions that would be best treated elsewhere, such as long-standing back pain, sore feet, minor rashes, earache and insect bites.
“These issues shouldn’t be in A&E in the first place. Our A&E department is for those who have a life-threatening emergency. If you think you need to attend A&E, but it’s not life-threatening, you should consider the alternatives."
Mr Lightbody said A&E departments are there for those who need them and people with a genuine emergency should not hesitate in visiting.
Judith Park, director of acute services, said a minority of patients have been “engaging in behaviours and attitudes that are completely unacceptable” in the face of Covid-related limits on patients being accompanied to A&E.
"Any form of violent or aggressive behaviour towards our staff will not be tolerated,” she said.