If a vet isn't an option I would personally swap to paper towels as mentioned for now and continue just the raw honey. I have no experience with applying neosporin but raw honey should not be causing any swelling, and in fact should help reduce it.
<<< I agree , remove the carpet - raid the kitchen pantry and take some sheets of absorbant paper toweling from the roll , line the viv floor with this , and simply replace the soiled sheets AS SOON AS THEY ARE POOED ON - THIS IS IMPORTANT.
The carpet , like hair is very hard to keep germ free, it's a perfect medium for bacteria, viruses and fungi to colonise. (Large effective surface area).
<<< I think you've been advised to use raw honey as an ointment , simply dab this on the inflamed toe and foot with a cotton bud as often as necessary each day, use 1/4 strength betadiene in water soak the infected toe and foot for about 15mins each day , this will help kill any biofilm.
<<< beg , borrow what ever it takes - find the money or way to get him to a vet ASAP. (maybe get a parttime after school job at a burger place, or on the checkouts at a shop if mom and dad refuse to pay for a vet. Maybe start a GoFundMe account linked to FB or what ever social media you use, do odd jobs ( clean the neighbours' cars, weed their gardens, mow their lawns, make lemonade and sell it, bake cookies, cupcakes, berry pies , sell them .... heck if you want to make $100 - $200 it should be dead easy now it's summer there.)
It's possible there is an infection and the raw honey should help with that. I'm unsure of how you're applying it, but I'd be careful not to actually contact the foot. When I applied honey to my dragon's toe I was almost kind of drizzling it on to avoid irritating it further with any rubbing.
I'd really recommend a vet but if that's not an option, raw honey. Please be sure the honey you have been using is in fact raw/untreated. Most commercial honey is heated and this destroys the benefits needed to heal the wound and does nothing more than make him sticky. Raw honey will be very labeled to clearly differ it from heated honey. It will often be labeled as organic and may boast that it contains the honeycomb as well.
If he's still eating and acting fine, he'll likely be fine as long as the wound is properly treated to stop any infection. Red and swollen to me says likely infected or at least very irritated, and the repticarpet may contribute to some irritation due to possible snags or some irritants in the fabric like bacteria.
You're well in the clear currently of any amputation, but that's worst case scenario for now, not death.