Shropshire Council has increased its testing capacity as the county looks to strengthen its response to the sharp rise in cases.
It comes after the county last week recorded its highest number of cases since the pandemic began.
Previously, anyone who had one of the main symptoms – a high temperature, new cough or loss of taste or smell – was asked to self-isolate and book a test.
But with more people testing positive who may have other symptoms, anyone showing any sign of Covid-19 is being urged to book a test as a precaution.
Additional symptoms include shortness of breath, headaches, aches and pains, feeling very tired for no good reason, sore throat, runny nose, sneezing and nausea in children.
Dean Carroll, Shropshire Council's cabinet member for adult social care, public health and climate change, said: "We are now at a critical point in our fight against the virus.
"Last week saw Shropshire record its highest ever number of cases since the start of the pandemic, and our local hospitals are really starting to feel the effect of the rapid rise.
“Effective testing for Covid-19 is one of the first lines of defence in reducing infections.
"Most people display at least one of the three key symptoms, but symptoms can also include shortness of breath, sore throat, headache, fatigue and sickness.
“These are lesser known symptoms, but have been identified as being related to coronavirus.
"We have good testing availability here in Shropshire, so I would encourage people with these precautionary symptoms to book a test, even if it’s just for your own piece of mind.
"It remains important that people continue to socially distance, wash their hands regularly and wear a face covering in indoor settings.”
There are a number of testing sites across Shropshire which can be booked online at gov.uk/get-coronavirus-test or by calling 119. People can use the option of “my council has asked me to book a test” if they show any symptoms.