Hello NOtdeadyet!, welcome from me, too.
I have not used Blissel myself, but it can take quite a long time to see improvement with any of the VA treatments, so it is very early days for you. I note that the PIL for this product says the initial loading dose is three weeks, rather than the one week you have been prescribed. The loading dose for most other products is usually two weeks. However, maybe your GP had her reasons, and she sounds as though she is reasonably on the ball compared to some others.
As to the soreness you are experiencing externally, maybe an emollient (eg Epaderm or Hydromol) or an oil-based vaginal moisturiser such as Yes OB might help. Some find an ice pack can give relief.
There is a private Vaginal Atrophy Facebook support group that is excellent for advice and information (and sympathy!) which you might like to join. Several members use Blissel.
JP x