Welcome to ECF I highly doubt vaping "pure" cotton vs "organic" is going to make a huge difference in your health, you haven't irretrievably damaged yourself or anything. Our bodies are used to dealing with an impurity here and there, and "pure" cotton is likely on the safer side than some possible other options.
I'd agree on trying rayon as well which, as long as it's been handled correctly, it's usually fine. I use Sally's 100% cellurayon, which the only thing you need to be careful about is make sure you get the one labeled "100% rayon" or you may wind up with a cotton/rayon blend by mistake. It's forgiving, and I like it because it's easier (for me) to wick correctly, that and it lasts a bit longer than cotton.
I am guessing that it was far more likely to be juice gunking factors that turned your cotton ikky than necessarily the cotton itself. If you use high VG, dark or sweet or highly flavored juices, and/or NET tobacco or WTA e-liquid, you have gunking factors (wattage can make a difference as well, as well as they way that you wick it. I mean, maybe the cotton played a TINY role, but depending on how much juice you were running through your RTA, it may have gunked up more quickly than you were expecting. I really can only get 3 days out of a cotton wick, maximum but rayon lasts me much longer.
In case you are worried about rayon being "synthetic" well it is, in the sense that it is manufactured from cotton, much as paper is "manufactured" by wood pulp. As long as the manufacturing process is clean , rayon is really only a "synthetic" fiber in the sense that it is "extracted" from cotton and etc. So, high quality rayon doesn't seem to pose any major health risks.
Good luck with whatever you decide. But, again, I highly doubt any damage at all by your brief "experiment."
Anna