While there are crude forms of home remedies that include such things as building a homemade toenail brace in which splints are used to try and relieve pressure there's really no reason why if you live in any kind of civilized area that you shouldn't take advantage of the simple over the counter solutions that can be found at most any drug store or via ordering online. The very fact that you are almost certainly reading this post online means that I know you have at minimum access to ordering the products you need online.
The most important thing to keep in mind before attempting any sort of home remedy of this sort is that you absolutely don't want to make your predicament dangerously worse by causing a dangerous infection.
Now that the disclaimer is out of the way the single greatest piece of advice that I can give to anyone dealing with this sort of issue whether it's their first encounter with a really bad ingrown toenail or it's a recurring problem and I'm speaking to someone who feels like they've tried every other conventional ingrown toenail products the answer is always simple, one word: Outgro.
For a detailed explanation of what Outgro is (it's a topical solution) please see the post specifically dedicated to this topic titled: Outgro ingrown toenail.
Warning: Do not do this (pictured above)At the very least get some over the counter medication and please never resort to this disturbing picture.