He is correct about the lymph fluid build up, which can become permanent for a while, turkey neck too under the chin too, leather neck, but may eventually go way on its own when fluid slowly channels out, most of mine did. I never heard of pinching the skin up and down per say, but did hear, read, about lymphatic lymph drainage massage, by a licensed practictioner, that has to be done in certain directions, circular motions, certain pressure on the neck, near the ears, face, whole body too, which may include skin pinching, and cupping, and Myofascial Release Massage too. I never practiced it on my own, not wanting to cause harm, do in the wrong direction, and was never really cancer free for more than a few months, so I didn't want to cause any extracapsular spread or damage my carotid artery, which can occurr from manipulation, even by a chiropractor. If your doctor gave you the clear, maybe look into Physical Therapy, and or a Licensed Lymphatic Drainage Massage Therapist, Myofascial Release Massage Therapist. As far as my concern, only my ENT is touching my neck lol.
Other things also help with lymph drainage. Light exercise like walking, swimming, swinging the arms overhead or heart level, which can be done while walking, a trampoline (caution with that), steam room, sauna, hot bath, sweating. Medication, toxins, chemicals also back up the Lymphs, so eating a healthy balanced diet may help too.
Good luck with everything.