If photons are the carriers of the electromagnetic force, why isn't electricity made of photons?
Who says it isn't?
I'm being a little facetious here, but the question "what is electricity made of?" is very philosophical. We often think of electricity as being made of electrons; but for example, in an electrolyte solution it may instead be carried by positive or negative ions. And in principle you can use any moving charge -- instead of electrons you could use muons or positrons. And when electricity travels through a capacitor, we speak of "displacement current", but no charges pass through the capacitor at all, electrons or otherwise; only the electric field changes. And when current in one side of a transformer induces current in the other side, again no charges go across; only the magnetic field changes.
So in all these cases, there is electric current; but it's not necessarily being carried by electrons, or even by moving charges in any obvious way. What IS always involved is the electromagnetic field, in every single case.
The involvement of "photons" is trickier. I'm not a particle physicist, nor do I understand QFT. (Nor am I really any kind of physicist, although I have a minor in physics on my computer science degree.) But ultimately the electromagnetic field is "really" a field; sometimes it's easiest to think in terms of particles, but sometimes it really is not. At relatively low frequencies, like you see in lots of electric circuits, the "wavelengths" of any "photons" involved might be measured in kilometers. That feels to me like it's very hard to think about. (The speed of light, in appropriate units, is 300 megahertz * meters. If your AC signal is a sine wave at 60 hertz, the wavelength of the "photons" involved is around 5000 kilometers, a little less than the radius of the Earth. Those are very squishy and delocalized "particles".)
On the flip side, though -- when your signal frequencies get very high, it starts being very reasonable to think about photons. If you have a 100 meter long coaxial cable, and you're using it to transmit a signal at 30 gigahertz, now your photon wavelength is just a centimeter, which is a tiny fraction of the distance your signal is going. In this case, we can talk about the cable as a long cylindrical "waveguide", and we talk about the "propagation modes" of the photons traveling along it. There of course are still electrons moving in the central and outer conductors, but we often think instead about photons traveling in the dielectric (the insulator) between the two. Of course, photons going through a dielectric medium like this behave differently than they do in vacuum. But not that differently -- the effective speed of light (the speed of signal transmission) in coaxial cable is anywhere from 2/3 to 90% of the speed of light in a vacuum.
(If you want a slightly clickbait treatment of this concept, take a look at this Veritasium video: https://youtu.be/bHIhgxav9LY You can see in the preview the clickbait lede of the video: "Electricity doesn't flow in wires". This is precisely about the conception of electricity as being carried by the photons, in the insulators, rather than by the electrons in the wires.)
And if we then attach the coaxial cable to an antenna, we really start considering photons pretty seriously. In the cable we try very hard to keep the photons contained, and interacting only inside the cable, but the antenna's purpose is the opposite -- to "leak" photons from the electrical signal into the air, in preferred directions, as effectively as possible.