My guess would be that you're trying to produce the fry from too high in your throat. Straining and constricting your throat in order to produce fry can be very harmful to your voice in the long term.
Think of bellowing, shouting very loudly or sighing - when done effectively, this comes from the chest even if it is distorted. It's the same with vocal fry. To practice the technique required to produce a death metal-style growl, you need to start with the same type of exhaling you use when sighing or huffing. To be honest though, video tutorials on sites like YouTube would be a better place to go to look for information on this - just make sure you look for someone who doesn't produce fry by constricting their throat. Even better would be to find a vocal teacher who can instruct you one-on-one so you don't hurt yourself.
Producing fry when you're not used to it is like exercising a muscle you've not exercised before - no matter what technique you use, it will ache a bit to start. With bad technique, you can really damage that muscle (or your throat), but with good technique you will be able to produce fry without much strain at all and with no lasting damage.
This is all coming from my experience as a metal vocalist. I'm not sure how Louis Armstrong produced his signature sound.