Is there a way I can play with someone, not over lan, and not over a sever on minecraft?

You have to use a server. I don't think there's any other way. If you don't want to make a server, find one with 0, or 1 person, get an open space with no one else, and start playing

If either of you have a fast-ish PC, you MIGHT be able to run the server on the same machine as the game. I don't know if this counts as 'making' a server to you, and it's far from ideal, and I've never tried it. Might work though.

The host will still have to configure their router / gateway to forward port 25565 to their box, unless they're directly plugged into the drop from the street (yuck.) So, a little bit of a hassle, but it's Minecraft.

Otherwise, no, Minecraft wasn't designed for a peer-to-peer architecture like that.