The sign for ringing as in "a ringing phone" (or an alarm) is done
by whacking (that is a technical term folks) an index finger
up against the palm of the non-dominant hand twice.
If you mean "ringing" as in my ears are ringing you might indeed see
some people sign: MY EAR RINGING using the above sign but if you are
taking about a hearing aid squealing then instead use an "E"
handshape near the ear and move it out away from the ear using a bit
of a wobbly movement.
You can learn American Sign Language (ASL) online at American Sign Language University ™
ASL resources by Lifeprint.com © Dr. William Vicars