A few disorganized remarks that may or may not be any help:

• Different people are good at different things. In particular, the algebra/analysis dichotomy is a pretty standard one and if you're good at analysis and not so good at algebra, it probably matters how good you are at what you're best at.
• It seems like simply not being fast enough could be largely irrelevant (if it's really just a matter of speed; the limiting factor in doing mathematical research is unlikely to be how fast you can do practice-test-level questions) or quite important (if what it really means is that you didn't understand the material well and therefore had to flounder about when someone with a better grasp would have headed straight for the solution). You may or may not be able to judge which.
• Motivation is really really important, perhaps more important than talent once the talent is above a certain level. One piece of advice I've seen (specifically in the context of academic pure mathematics) is that you shouldn't become a mathematician unless you couldn't bear not to. Because mathematics research is really hard, and it will kick your ass, and how successful you are will have a lot to do with how you cope when it does.

(My own background: got the PhD, did a couple of years of postdoc, was quite staggeringly unproductive, got out of academia and into industry, have been reasonably happy there. Probably happier than I'd have been as a struggling academic. Most academics are struggling academics, especially for, say, the first 5-10 years after getting their PhDs.)

Some questions you might want to answer for yourself:

• If you go to grad school, get your PhD, and then don't go into academia, is that a good outcome or a bad one?
• If you don't take the academic path, what will you do instead?
• Whichever way you go, regrettably there's a very good chance that you won't end up revolutionizing the world. If you compare possible academic futures with possible non-academic futures, and make the assumption that you do just OK -- which feels like the better outcome?