No, we do NOT all have parasites. This notion is perpetuated by quack doctors who are generally quite happy to sell you products and supplements.
Colon cleanses and enemas can do great harm to your intestinal tract. As for the parasite "cleanse," it is not much more than an herbal laxative, and would not remove parasites if, indeed, a person were to have parasites. If you wish to use these products on yourself that is, of course, your choice, but they aren't recommended and won't cure anything. Eating a better diet is a really great move, though. We should all strive to do better at that.
To the OP - never put alcohol on your testicles. As you noticed, it burns like fire when applied to thin or broken skin. As Paxiled mentioned, it won't cure anything either. It is quite possible that you have a fungal infection, and there are many over-the-counter creams to effectively treat those. There are basically two types - one that is intended for jock itch, and one that is intended for athlete's foot. They have different active ingredients, and one of the two usually eliminates any minor skin fungal infection. You could start with the jock itch cream, and if that doesn't help in a few days, try the athlete's foot cream. Neither cream will hurt you.
If at-home treatment doesn't provide relief, a visit to the doctor is in order.
I think using rubbing alcohol on that isn't going to help you any and probably irritated and dried out the skin. When you have a problem and don't know what it is, you can't really treat it, right? You either need to know what it is because you had it before or you need to see a doctor and get a diagnosis. With a diagnosis, there might be several very different treatment options, but you can't know which ones unless you know what you're dealing with. If this is ringworm, or jock itch, which is common, the treatment might be medicinal or natural but it wouldn't be rubbing alcohol. See someone who can diagnose this kind of thing before you start treating it.