You're asking for a casual (not legal) assessment of your situation, so here goes; but keep in mind many attempts to remedy your situation may involve legal decisions that you need to make on your own.
Basically, you need to determine company policy regarding employee health and abuse by customers; document incidents and conversations; and look outside the company for other resources.
First, you are bound by your employee contract and handbook and any remediation language in it; so read that and any sections that have to do with health and working conditions and what recourse you have with the company and your immediate management. You should talk to your supervisor and others up the chain of management about what is happening with your work environment.
And when you do, it's a good idea to document what is said, either at the time in your meetings (written notes; ask permission to digitally record), or afterward in your notes. (And document if you are not allowed to document.)
It's a good idea to document a few days of your customer interactions, unless your employee handbook forbids this. Don't use real names or customer IDs, but write a few general sentences about each interaction for use later in mediation or legal venues.
Outside the company, a Google search will give you information about a human rights commission or NGO in your state that deals with worker rights; contact them about the rights you have that supersede any company policies.
And a quick Google search for "Verizon working conditions" gives lots of information and various NGO sites dealing with Verizon and unionizing, outside support systems for Verizon employees, possible on-going and current litigation against Verizon, and more.
Lastly, there are attorneys who would do a no-fee initial assessment of your situation; check the web or the phonebook.
Your situation appears to be sadly common, but take some legally permissible steps to get help from management and outside sources.