Assume you have plugged the headset directly into the handheld. Do you have
a push to talk accessory?

You can try clamp on ferrite beads on the headset. Generally close to the
radio. Sometimes it helps to wind a turn or two through the ferrite (but
that reduces the length).

Any extensions of the headset cable could make the problem worse.

Wrapping the headset cable around the antenna is a bad idea.

You can remote the antenna with an extension cable. That should remove the
rf from the radio. If you do that, provide a groundplane for the antenna
and keep it vertical.

Colin