There are a ton of companions. Mainly you can get them from doing the guild questlines (mages guild, companions, etc) or you can get them from doing the Jarl's questlines in the cities and get new housecarls.
"If the facts don't fit the theory, change the facts." - Albert Einstein
In the first town you go to, there's a quest you can do involving giving a letter to a girl. I'm not sure if you did that yet. It's fairly easy. I'm not sure if the companion you get depends on the decision you make when giving the letter. When I told her the truth, I got this guy named Froental, looks like an elf archer. I haven't checked yet since I don't need him atm. But you can ask him to follow and such.