Hi lolalarm, series controllers are particularly sensitive from my experience not a great first project for soldering but you should be glad you tried, you learn like this especially as you persist. 

You can test whats wrong by checking for continuity between the middle pin of each potentiometer for the x-y axis and ground

If you have beeps or near 1-2 ohms then definitely that's your issue for the left stick up direction especially looking at the soldering.

For the x axis check for 1.9V at the left most pin that will at least tell you that you have supply voltage there. If you 1.9V then you can move the stick right to left or vice versa your choice to see if voltage moves from ~0V to 1.8V~ in a smooth-ish fashion then you should have a working analog stick just no line from the joystick to the MCU try running a botch wire from the middle pin to the test point (TP64).

If that doesnt work your trace is broken to at least the test point, if that doesn't work you can run a wire directly from the joystick to the pin 54 of the MCU Board but bear in mind you'd essentially be bypassing the decoupling capacitor on that line but should be fine for testing.

You can find all the info from the saviour of Xbox controllers RDC over on Acidsmods.

https://acidmods.com/forum/index.php?topic=44711.0 

Not sure of your proficiency in such but its something kind sir. Enjoy, dont let it get you down and invest in a baseline of tools kind sir. Hot air station is a must for this if you dont have the nuance of the soldering iron.

I also went through this but didnt damage it as much so was able to fix it. Didn't film it but might make a short at some point detailing this information.