phone neck
n. Neck pain caused by holding a telephone between one's shoulder and ear for extended periods.
Like most Homo sapiens, I have 10 fingers (in need of a manicure), 10 toes (that could look a whole lot better), and at least 10 kinks in a back that aches for regular TLC. Ah, yes, the modern white-collar ailments: Computer spine and phone neck.
—Staci Sturrock, “Get thee to a spa,” The Palm Beach Post, January 31, 2002
1989 (earliest)
Nobody can blame Don Von Hemel if he happens to have a terminal case of phone neck — that affliction which strikes those who spend hours and hours reaching out and touching someone.
—Jerry Shottenkirk, “Von Hemels Stay In Touch, on Track,” The Daily Oklahoman, February 27, 1989
This afflication is also sometimes called telephonitis, but phone neck is more pleasingly descriptive. A variation on the theme is cellular phone neck, implausibly caused by a driver jamming a phone between his ear and shoulder so that he can keep both hands on the wheel. (These days, it's more likely that he has just one hand on the wheel while the other wields a coffee, operates his car's onboard navigation system, or vents his road rage using the appropriate finger-based signals.)

People have been using this phrase (and making the requisite "pain in the neck" jokes) since the late 80s.