I don't know if cayenne pepper would help now. The general idea with cayenne is to damage the oocysts that carry blackhead before it infects the birds. Also, if you're treating with drugs, best to not mix them with anything, as the results are often not great. You can of course try anyway, if you feel it's best. Sometimes what works doesn't seem to make sense for even hundreds of years. Explanations can be a long time in coming.
My own preferred treatment for blackhead is maybe not something you can access, but I don't know so will share it anyway. I give them a cup of raw cow's milk, not pasteurized or homogenized, that's had a teaspoon of honey mixed in and has been left to sit for a while and then had the fat scraped off the top.
That does it almost all the time. Sometimes it takes two cups. A very small percentage die anyway.
Giving them heat-treated or homogenized milk could be fatal since their liver is severely compromised with blackhead and the fats can kill them. I've tried giving it to them without scraping the fat off and they would rather die. So to speak; I just mean that they just refused it as a rule until I removed the fat. For this reason goat's milk may not be ideal as it's naturally homogenized. But I don't know for sure, I'm just saying what's worked for me.
If the bird is not eating, don't try to encourage it to, and don't force feed it, as fasting is one way the body defeats disease and force feeding is often more harmful than helpful. If it won't drink the milk, dip its beak in it (not up to the nostrils, but just so it gets a taste on its tongue) and then it will drink it willingly --- IF it has blackhead. But honey plus milk is great for many other issues too as it's readily bio-available protein, electrolytes, nutrients, cal-mag and so much more, which is just what a stricken animal often needs to tide it over.
Most grains are dangerous to birds with blackhead, so no corn, no sorghum, no wheat, no sunflower seeds. Rolled oats and millet are not detrimental in this stage, so it can eat those if it likes. Even once a blackhead sufferer is back on its feet, keep it on a simple, raw diet for at least a week, preferably a month, as it heals its internal damage; lots of fresh green grass, natural proteins (not pellets), are best. Hardboiled egg is a great recovery food, but raw is good too, if the bird wants that form of protein. Insects would be great unless they're the sort whose natural defensive mechanisms involve chemicals which are no trouble for a normal bird's liver but could do in a bird with a weakened and damaged liver.
None of my chooks have died from blackhead though, so I'm speaking about the treatment I've used on turkeys. I did have one rooster who was dying from something else get blackhead twice in a few days, but he was over it again almost as soon as the symptoms showed.
I give them fresh raw garlic regularly and kelp as well and that seems to take care of it. Only my turkeys were susceptible for a while. I also give my birds lots of herbs on a regular basis including cayenne, which helps with many diseases and potential heath issues, and I lime the grounds they're on a few times a year, so that also helps destroy blackhead and other parasite and diseases.
Just to be sure it's blackhead, can you describe the symptoms, including the poop's appearance? Heart failure can also look like blackhead, and so can a few other diseases or problems.
Best wishes.