In a word – yes.
Yes, it is possible to still spread COVID-19 if you test negative but have cold-like symptoms. This is true if you just started having symptoms, as well as if you’re testing negative after a COVID-19 infection.
Rapid COVID-19 tests are quite good at telling if someone is infected and can spread the virus to others. However, these tests are not very good at detecting low amounts of the virus and can show a negative result even if someone is infected. This is because early and late in the infection the amount of virus present in the nose may be very small, not enough to test positive but possibly enough to spread to others, especially if symptoms are present. So, if someone has low amounts of the virus, they may test negative but still be infectious, especially if symptoms are present.
Also, at the start of the infection, the amount of virus may be very small but can rapidly increase over a matter of hours. Because of this, some people may test negative but then positive several hours later. With a positive test, it is important to then isolate to prevent spreading the virus. If you get a negative test but have symptoms, remember to use extra precautions and test again later, as you still may be infectious.