A metal radiator might ground you.

Internet says to touch the screws on a light switch panel.

If you really don't have anything metal in your house (metal sinks or any appliance with an outer metal shell that should be grounded), grab an extension cord, cut it and completely remove any cable that is not the yellow and geeen one, that is the earth cable (assuming in Australia that is the correct color scheme), expose that wire and touch it to discharge. Make sure the other cables are in no way exposed. If yoy want to be extra safe, buy a plug and only connect the earth cable.

/s of course, don't do that unless you know your way around AC power

Can you touch the wall with your full palm before touching your pup and see if that helps?

I too live in a hilariously dry climate in the winter and become a human lightning rod for several months at a time. Here’s what helped me: a quarter! I carry a quarter in my pocket all winter to touch to metal (I deeply hate getting shocked myself, especially the huge static charges). You’ll need something made of metal that is grounded, though. We have metal shelves or the aforementioned light switch screws. You can also look for screws on your washing machine, doorknob, dishwasher, sink, etc. Anything with a little metal should work. Then - touch the quarter to it, hear (but don’t feel) the zap, and enjoy your dog with no fear. Hope you can find something metallic somewhere in your home!

Simple, just touch the ground. That's what your dog conducts to. Just take the dog out the equation.

Do you have a desktop computer? If so, and you know where the power supply is, you could touch the metal grate on that. The power supply will be earthed due to requiring a ground, and the cage itself is properly made so maintenance can be done safely by connecting an ESD wrist strap to the power supply cage.

If you don't feel or hear a shock, you have not discharged.

If you have more patience, you can wash your hands for 2 minutes and you wouldn't be statically charged. Though, that may be really cold as an after affect.

Oh man, I feel this one. I moved to a colder climate with my cat in winter and every time I pet her, if I got close to her ears... zap. She was always like ?????? About it.

One day it just stopped happening one day and I'm not sure why. So I don't really have any advice.

You could try rubber soled footwear instead?

I usually go with the light switch/outlet screw but you said those are covered. There must be grounded metal somewhere in your house. The microwave body, a pipe or faucet, you could even get one of those grounding wrist straps that plug into the ground port on your wall socket.

Why do you wear boots on the couch? Or indoors at all?

This happened with my cat often enough that once I went to pet him and saw him wince from my hand 😢

So after that I started doing the same things suggested here Try touching stuff around your house to see what discharges you, but also what I got in the habit of doing was tapping my cat on the back haunch before petting him. That discharged me in a much more manageable place for him and then subsequent skritches were still pleasant and appreciated.

I've tried for years to figure out how to lower the static electricity in my house, but keep coming up empty. I think it's the combination of rubber-soled slippers, carpeting and anti-static mats in the office. So at my desk, I have ran a thin sliver of tinfoil along the edge and grounded that, so when I sit it discharges through there instead of my computer.