Entitled to Unemployment for good cause

What is the name of your state (only U.S. law)? North Carolina
I was hired as a retail store manager and I informed my employer of limitations I have due to a shoulder injury and past surgery(rotator cuff tear & repair). After 9 months of employment I am being told I have to make sure a huge tent is put up in front of the store because they do not have a sign and want to attract customers. I told them I could not do it and they told me to get volunteers who sometimes help at the store but are not always dependable and sometimes don't show. It takes 3-4 people to put up this tent. I got a written warning that if the tent is not up every day I will continue to get warnings and my job will be terminated after I receive 3. I was even told to go to the business next to us to get them to help put up the tent.
I want to quit because they say there is no exceptions. I do not want to do any more damage to my shoulder by trying to get this tent up if I don't have any help.
My question is, if I quit, will I be able to collect unemployment until I find another job due to the fact that I want to quit for good cause?
Thank you

No. That may be a good reason to quit, but it is not good cause to quit and collect benefits.

I am not wanting to quit to collect unemployment. I want to quit to find another job. I just wanted to know if I am untitled to unemployment benefits until I do find another job.

No. If you quit you would not be entitled to unemployment until you find another job.

I don't know how to make it any more plain than that.

{Quote}I told them I could not do it and they told me to get volunteers who sometimes help at the store but are not always dependable and sometimes don't show.{Unquote}

The situation is very clear. You want to weasel out of the job assigned to you by blaming the volunteers the company wants to help you, but who you claim are undependable.

It was suggested that you go to the business next door to get help, but you have the gall to complain about not getting help when you apparently haven't even contacted the business.

You don't have good cause to quit and collect unemployment when you haven't made a good faith effort to get the job you were assigned - getting the tent up to attract customers - done.

And - just to clear up the last point. If you quit due to a medical condition, you are also (likely) not entitled to unemployment. Disability perhaps, but not UI.

Hopefully, the OP would receive nothing due to the circumstances of his quitting. If his employer had expected him to put up the tent by himself even though aware of his medical problem, it would be one thing. He has access to help putting up the tent, but either makes excuses for not using it or ignores it. I would hate to see him be rewarded with taxpayer dollars for not even trying to do the job.