I didn't kill a noble, I killed a random woman and the guy who lost his dog. And, ironically, this all started happening after I went to the cave near Morthal - I did the Solitude quest next, so I never even thought about the vampire thing... Didn't even realize I was vampire for a while and didn't know what was happening... Again, noob TES player here... Thought I'd try it due to what looked like awesome gameplay and graphics... I grew up on Intellivision and actually still play it sometimes today, actually did 2 days ago and played Frog Bog, how about that?

So, how do I fix the vampire thing? Go back to Morthal and talk to the guy that I saw before?

You'll find everything you need to know here -
http://elderscrolls.wikia.com/wiki/Vampirism_%28Skyrim%29

Try to sneak into somebody's house and feed off them at night - people will stop attacking you.

If he is a vampire, he should talk with Fallion in Morthal. he's the only one who can cure you from vampirism.

I have been killing Thalmor patrols left and right without incident. Of course I always "confessed" first.

I finally fed on someone since I found out I had been a vampire for 10 days. I tried to see Falion at night and he called the guards on me, so I left. Then, I came back around 8 AM when the door was unlocked and he chased me away again... I think I had me weapon sheathed... What am I doing wrong with him?

FYI, to whomever may read this... I did go back to see Falion, and it worked. I had to cast soul trap on an enemy and then defeat them to fill the black soul gem. Then, I saw Falion and I met him just north of the town, slightly west, at about 6 AM the next day. Everything worked, and I don't get attacked by anyone anymore... I am wondering, if you kill someone while a vampire, does it count against your bounty when you transform back? I didn't have any issues anywhere, which was nice... However, fun times trying to get Falion to complete the ritual while a dragon is circling overhead...

Yes, this happened to me. Now I can't go to Riften without killing half the population in defense. Riften is now useless to me.

I haven't exuasted all the options though. I still expect that there is a way to fix this. Gonna try again today.

There is indeed a criminal bug related to thalmor soldiers. had same thing happening in Riverwood once. Luckely it remained only in Riverwood. Freed a prisoner from patrolling thalmors on the way to Riverwood, this should not be considered a crime. Killed the three treehughers and when i entered Riverwood all citizens suddenly attacked me, even the ones i did quests for. Guards did nothing, even if i killed them, i had no bounty.
But i didnt mind much, happened on my dagger backstabbing murderous orc. So didnt pay much attention to it untill i read this topic, there has to be some Thalmor bug that triggers this.

The trick is to provoke them into attacking you first (tell them you worship whomever you please etc) - then there is no bounty. If you trigger hostilities by attacking them first, before they become hostile, then there will be problems - I could equip a massive army with the Thalmor armour I've 'procured' - and have zero bounty