There is a sort of gumbo in your question:
- How do I know if I fit my frame"
run the French fit program and see if you are close.
- How can I spin on hills?
Do you spin on flats now, is it just hills with a loaded bike that you can't spin up?
Are you locked in a death grip, by whatever technology, to your pedals? You can only pull in a circle if your footing allows it.
What you are describing sounds exactly like you are just geared too high. For a normal all around fit person, who has basic cycling technique, the easiest way to go up hills is spinning. I think I spin all the time, but when I hit a long hill I really notice the extra power I get from ankling up the hill. It is a mater of survival, I'm just not fit enough to do it any other way.
When you need to get out of the seat, it is normally you need more power. If you need more power it is because you aren't geared low enough. I do find, though, that I just can't pedal "backwards" enough to get up a hill. Even in the seat I have to draw the line and fight at some point or I will just keep loosing momentum. That is why I am spinning so hard. I am reaching out to muscles I don't normally need to just cruise along. Or at least they are muscles I get sloppy enough not to always recruit.