I think I cut an ingrown toenail wrong and made it worse

Not my finest hour. The side of my big toenail has been sore for about a week and last night I decided to sort it out myself with the nail clippers and a lot of optimism. I got a bit of the corner out, and now it is more painful than it was before and the skin next to the nail is red and puffy.

It is not oozing or anything dramatic, and I can still get a shoe on, but I have clearly made it worse rather than better.

What is the right thing to do from here? And what should I have done instead, because I would rather not repeat this on the other foot in six months.