Etsy sends emails when they suspect suspicious activity. I've had those emails when I got a new computer. When my Internet switched towers. When I used my phone during a recent power outage to put my shop on vacation.
So you should be receiving emails about such activity unless your provider is blocking them.
Since you have no listings and no about page which describes what you do, it is hard to say if there is another issue at paly here. A look at a cached versions shows vintage items. It is possible you are getting caught in the named designer issue. Do your items have the provenance to prove that they are from the designer and not a fake? Have you looked for your photos elsewhere and issued takedown notices if needed.
Are you receiving notifications from Etsy about possible issues? Have you checked your service provider to make sure emails are getting through? That can cause suspension if Etsy sends you an email and you need to work with the holder for an IP issue?
Do you have security on your computer? That can also cause issues. If using a VPN, that makes life with Etsy more difficult as Etsy system seems not to like most VPN's.
The glitch may lie not with Etsy but with your computer and ISP. You may need to ask your ISP for more information on security that they may use and if it is interfering.
