Creating a font for a made-up language

Hi, I have literally no experience with anything even remotely to do with graphics, but just as a bit of fun I was wondering if anybody knew of a site where I could design custom characters for my own language and assign them to my keyboard to type with? I've found lots of sites where you can redesign letters of the English alphabet, but the tricky part is that in my language each letter has about 5-7 different variations (mostly different accents). As this is just for fun, I don't really want to be spending money on this, so I'm just looking for some free software I could use to design characters and then determine which keys on my keyboard will produce said characters.

Hoping this is possible, but if not no worries, it was just an idea I had that I thought could be kinda cool. Thanks!