Shaver recommendations for a very close shave

My dog has a lot of allergens and is very prone to skin infections. After a very protracted series of vet visits, she's on daily medication and we've done an allergen test to figure out what she's reacting to. She's also being bathed daily to help clear any allergens from her skin. The vet especially recommended we keep her shaved completely, even the insides of her ears, her paws and tail, to prevent allergens from getting caught in the fur and to help air her skin since it's very inflamed. They did it for us once before sending her back to us and it's a very close shave, like almost to the skin.

I've tried a few pet grooming kits and a cordless Wahl's shaver for this, but the grooming kits don't get remotely close to the skin and the Wahl's shaver kind of gets caught on her fur since it's thick and there's a lot of ground to cover. Is there any recommendations for a good shaver that can keep up with this sort of demand? I have to shave her weekly/fortnightly to keep her fur down.

Any help would be greatly appreciated. Thank you!