Why do I change into a vampire?

You could have contracted the disease Sanguinare Vampiris, which turns you into a vampire after a few days.

See the elder scrolls wiki for other causes.

And as shanodin explained: if you become a werewolf, you cannot become a vampire anymore (unless you cure yourself from Lycanthropy of course)

From the wiki:

Sanguinare Vampiris is the disease that eventually culminates in vampirism and is typically contracted when attacked by a vampire, either with physical attacks or being subject to their Vampiric Drain spell. If one is attacked by Vampiric Drain, there is 10% chance of infection.

Also, if you have Dawnguard installed, it can be contracted by drinking from the bloodspring in Redwater Den.

There are multiple ways to cure this:

1. Cure disease potion

2. Activating any shrine

3. Becoming a werewolf (talk to Aela The Huntress)

4. Going to Falion in Morthal

5. Console commands: From the wiki:

   Another way of curing vampirism is via console commands; open the console and type, setstage 000EAFD5 10. By using the console command code showracemenu to change the Dragonborn's race, vampirism is immediately removed. This is also true of the changesex command.

It should be noted that the first two methods only work if you've not yet become a full-fledged Vampire (in the first 3 days after contracting the disease).

You get this by going into Vampire locations (one I found is during A Deadras Best Friend with Barbas) There is roughly a 10% chance of catching this Vampirism. You can figure out if you've contracted it by going up to people they may say 'you don't look to well' or something like that. You can also check in your currently active magic spells on the menu. When you first contract it, you can get rid of it by going to a shrine (Mara, Talos, ECT.)