Preface: You actually describe two problems-- a rootless, groundless character that doesn't seem amenable to goals, and the self-spoiler issue. I'm going to try to address both of those.
I have been in, and been running, PC-goal driven games for a long time. Sometimes they are pure PC-goal driven, other times, they are half-that and half-GM over-arcing plot. In that time, I've found three separate things that help, but which really work best when all employed at once.
1) As a player, be willing to work with your GM.
This sounds trite, and if you read this site you will see "talk to your GM/player" coming up as a frequent refrain. So I want to emphasize that in this case, I really mean it, and I really mean work, over an extended period of time, not just have a little chat.
Start out wherever you feel comfortable.
It might be an admission that you're flailing for suitable goals because you accidentally came up with a character that is rootless. (I've done it.) Or because you don't feel like you have a good handle on the background. (I've been on both ends of that, player and GM.)
It might be you have some ideas and you're not sure if they're appropriate, so it's more of a brainstorming session. It might be a request to add a little hitherto unknown depth to your character's background so he's not so disconnected any more.
Hopefully your GM is willing to help out at least a little bit in this regard, since this is not just coming to the GM saying, "I can't do it." I certainly would be; it seems odd to the point of perversity to watch a player flail and not help.
2) As a character, be willing to care about something.
Your character background is not constant. Just because you start with the goal, "Walk the earth, healing and curing, building a movement," doesn't mean that's all your goals ever are. At some point, they can (and probably should) either sharpen and focus on specific aspects of those goals, or fall away and be supplanted by new ones.
Either of those is okay!
If you came to be as a GM and did step one above, and also confessed that you were worried about self-spoilers, I would spend a few sessions drawing out some possible goals and conflicts for you. But I would expect you to meet me half way. I would expect you to be observant and if at all possible pick one or two.
3) As a player, set open-ended goals, and don't worry about spoilers
Knowing the type of goal you have is more or less knowing the object of the current quest. It's not inherently a spoiler, any more than Frodo knowing he has to destroy the One Ring is a spoiler for The Lord of the Rings. The spoiler is how it plays out in the fateful moment and what built up to it.
However, some people really are genuinely more sensitive to spoilers than others.
In which case, suitable goals are more like, "Learn more about X," and "Make progress about Y," and "Bring closure to Z." Note that none of these specify anything about the result. None of them specify what the end state looks like in detail.
If a raging debate between your followers is between some rival branches of heterodoxy, then "bring closure" could be your character finally endorsing one, or the other, or laying down the law on orthodoxy and dealing with the consequences of any of those choices. I've had great success with this approach as a player in PC-goal driven campaigns, even though I'm not troubled by the kind of self-spoilers that you are.
(I will note, this does presuppose a game world rich enough that these more meta options make sense.)
