Oh buddy that's really pretty bad, it's not at all an infection I would wait around on or try to treat from home. Honestly in my own opinion he simply needs an amputation of his tail a bit above the visible infection. It's not a big deal, they should be able to do a local anaesthetic and then do the amputation, stitch it, dress it, and give antibiotics and pain meds.
Here's the issue with his tail: it is actually an active infection, and it looks very aggressive, and is moving right up his tail. It's extremely swollen and I actually don't see much necrotic tissue yet, but you're correct that an infection that bad will definitely continue to spread up his tail towards his body, and can invade his bloodstream at any time, causing a systemic infection, or sepsis. If and when that happens he will absolutely die without strong IV antibiotics. There isn't anything at all you can really do to treat this at home because the infection needs to be attacked internally, not just with topical antiseptics like Betadine and creams like Neosporin.
His tail is very, very raw and very swollen, and he's in a lot of pain. A vet, even a general vet, would be able to give him some pain meds and antiinflammatories, along with an antibiotic injection and oral antibiotics. If you went that route, which is the least amount of treatment you'll be able to maybe get by with, it shouldn't cost much more that $100-150. The problem with treating that infection medically is that if the infection is too far gone to be treated medically, then you'll also have to have it amputated, which is why I say that an amputation above the active, spreading infection is the way to go. It's quick, less painful, and is pretty sure to get rid of the problem. And a simple tail amputation, antibiotics, and pain meds should cost somewhere between $150-$200.
Can you make monthly or even weekly payments? You need to be proactive about this because that infection is spreading quickly, so you need to start calling around to vets, explain what the situation is and tell them that you can put $100 down and make payments on the balance, I can't imagine that you won't find a vet willing to treat him and accept payments if you put $100 down, because the balance wouldn't be much.
CareCredit is the other option, go to
www.carecredit.com and apply right online, you'll get an answer immediately, along with an approval paper you print out with the limit they approved you for. Pretty much all vets take it, and once you get that approval you're immediately able to take him to the vet. Then you just make a monthly payment to CareCredit. So if you can't find a vet willing to take the $100 down and accept the rest in payments, then the CareCredit is your backup.
Either way he needs to get to any vet at all by the end of this week at the latest before that infection spreads into his bloodstream and his tissue does start dying. Forgetting for a moment that he'll eventually die from this, he's gotta be in a whole lot of pain right now, and even though I know you're trying to do everything you can for him from home, there's nothing you can do at home externally or topically to treat an infection like this, and he needs prescription pain meds in addition to the prescription antibiotics.
Keep doing what you're doing with the Betadine and topical Neosporin or triple antibiotic ointment so that it's kept as clean as possible at all times. Hopefully it will slow the infection from spreading so quickly so you can get him to a vet...Good luck, and if we can help in any way please just ask.