There's a number of things you can do in ESO as a low-level player in Cyrodiil.
Firstly, you can participate in various forms of PvE content throughout the zone. NPCs are all level 50, but the game does scale your stats to 50 as well, so you'll be able to fare okay. There are a number of dungeons, PvE quests, Skyshards, etc. in Cyrodiil to keep you busy, if you find you're not doing well in PvP right now.
Secondly, you can try to find a group of other players to join. There are usually groups of some sort advertising in Cyrodiil, and having other players to back you up can help even the odds in PvP, or even tip them heavily in your favor.
If you don't want to find a proper group to join, you can also try joining in on a siege. Whether defending or attacking, there will be plenty of players on each side of the conflict, and so plenty of support/buff/heal abilities being thrown around if you need them. The larger number of players also can make it less likely you'll personally be targeted, assuming your side is greater in number.
If you really do want to solo PvP in the zone, there's still a few options. The simplest is to leave for a few levels and come back; at level 15, you gain access to the weapon swap mechanic, and with it you also get a whole second bar of abilities to use. This one mechanic alone can make a huge difference in the performance of some builds. Also, in the early levels, you probably haven't got all your abilities morphed yet; holding off for a few more levels to get some of those upgraded (especially if you're going for morphs on abilities that add healing) can have a big impact.
You should look into improving your ability to sneak. If you're a Bosmer or Khajiit, or using Medium Armor, there are passive abilities in those skills which can help. Even without them, just learning to be aware of your surroundings, learning how close you can get before enemies see you, etc. are very useful in helping you get across Cyrodiil without trouble. A useful tactic is, upon entering sneak mode because there are enemies nearby, wait until you go undetected, then walk away from where you were in a somewhat random direction. Even if an enemy spotted you and heads to where they last saw you, you've since vanished, and it's generally not worth their time to hunt a lone player down.
Lastly, if all of the above isn't enough, you can try switching Campaign. Some of the campaigns can have lop-sided player populations, and if your own alliance is more populous in one campaign, that can translate into an easier experience while you get used to Cyrodiil and ESO PvP in general. You can either switch your Home Campaign, or just enter another one as a guest to get the hang of things. Just look at the little cell-phone-signal-bars icons in the list of campaigns to see how many people from each alliance are in a given campaign.
It appears I have gone and created more questions then I have answered.
First of there are 3 ways to level up once you hit Veteran Ranks; Veteran Overwold zones (questing), Veteran Dungeons (same dungeons you did while leveling but much harder) and PVP.
The short answer is more like your 3rd option. Not in the way you described it though. Level 50 A.K.A. Veteran Rank 1 is when you are sent to the Veteran Overworld Zone, which is the Veteran questing area where you do the questlines of the other two factions. Only in these areas everything is Veteran Rank. Veteran NPCs, Veteran quests, Veteran Rewards, Veteran Gear, Veteran level resources, you name it, its Veteran.
If you so choose to go back to your home faction questing area the highest loot you will find is level 50. Nothing will be Veteran except for the occasional resource you might find in coldharbour that lets you make Veteran gear. And yes you can go back simply by teleporting.
Also the first time you do this, (speculation at this point) the questing will only put you between veteran 4-6 which you will then start the next factions questing zone. The idea behind Veteran ranks is to take a very long time.
Alright time for my long answer full of spoilers and such (this is my attempt at not causing more confusion)
So you have finished Coldharbour, foiled Molag'Bal's plot of destroying Nirn. You have just hit level 50 (AKA Veteran rank 1(hopefully, those that don't have to grind to 50 cringe)) Now you are being summoned to the harborage to fight molag'bal. Once defeating him you are asked if you wish to see what it would be like if you had washed up on a different shore, saved by a different faction. If you accept, you will start your journey through whatever faction the game chooses for you. I am unsure if it is random or if there is a linear path of which one is next. You start out just like if you had started out making a new character for a seperate faction, except you are still veteran rank 1 and still have all your skills and gear. Also everything is veteran as well as mobs which by the way are much harder to kill. Traps are just as deadly, one misstep will hurt, two missteps will be deadly. So if you couldn't help yourself and read this part of the answer enjoy veteran content its way more challenging and fun then normal mode.
Best Answer
Turns out it's a cursed necklace from a quest. You find a necklace on a skeleton and when you return it to it's maker he explains it encourages the wearer to essentially commit suicide.
Jeeze.