I'm 5'1. I've searched for stuff online about short guys doing pua but it's always people who are like 5'7 or maybe 5'5.

This kind of shortness is really debilitating.

I want to know if I have any potential. I feel that even if I try at this stuff, I'm going to still have to go through a harsh filter process.

Being short is definitely a challenge, there is no doubt about that, but it is a challenge that you can conquer!
I read this post by Warped Mindless and it was really interesting! met-the-most-ugly-pua-ever-inspiring-story-vt62802.html
Have a look at that!

Another great inspiration for overcoming challenges is Sean Stephenson, if you think you are challenged when it comes to physical attributes, just have a look at this guy. He is now very successful and often seen hanging out with many beautiful women! Here is a video with him talking at a David Deangelo seminar, the man is very inspiring and I recommend all of his videos!

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So yes, you may have a little harder time succeeding than other PUAs, but this should only inspire you to work harder, any one has potential to become the worlds best PUA, don't give up!
You can make your short statue in to a "thing" you can make it in to self-ironical jokes about yourself and be a really funny guy, you can also compensate for your length with tons of confidence. Another thing I want to emphasize is that you should ask for help from someone professional (at least once) when buying clothes and selecting a style so you buy something that brings out the best in you and doesn't make you look shorter!
Good luck and happy sarging!

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Slywalker

10 things I wish someone taught me about Pick Up 10-things-i-wish-someone-taught-me-vt53087.html

No doubt the cards will be stacked against you. But as you have good game and don't try and game a girl that is 5'10", more like a girl around your height you should be fine.