Whether it should or shouldn't isn't the issue. Without informing any of your current doctors of your intent -- your PCP in particular -- it could be construed that way, and it is far easier to get ON a list of doctor shoppers than it is to get OFF of one.

If you have a physician who does not listen and hangs up the phone on you, then IMO, you don't have the right doctor for you, and you should find another. Going to a walk-in clinic cold and asking for pain meds (regardless of whether you're asking for a referral to another doctor) is, IMO not the way to do this.

A better way, IMO, is to explain the situation to your PCP (who is the one to coordinate all other care) what is going on and request a referral from him/her for pain management, AND another neurologist -- this one isn't working out. Your PCP should be familiar with all of your records and medical history, and therefore, be the one to address your issue short term and refer you to someone who can help for longer term care.

Google: how to find a good pain management doctor

Did you go to the clinic, and if so, what happened?

Doc