widgeon3, priority slots are still available to those who have been shielding and are vulnerable, as long as you are registered with the LA as such.
I know, because I have had deliveries from Tesco every week since I started shielding in March.
It may be worth contacting the relevant department at your local authority, I have found them very helpful.
When I was finding shopping difficult at teh very beginning, I found Iceland to be very good. Have you tried them?
I too have Sjogrens, a compromised immune system and chronic lung disease. I do however, strive to wear a mask for short periods if I'm out. I acknowledge it's not easy and very uncomfortable for people with comorbidities. The worst part of wearing a mask and having Sjogrens is for me being very thirsty.
However, I'm trying to protect myself and others, as much as I can.
Yesterday I had my flu vaccination at the local football stadium and everyone was wearing masks.