I had a similar problem happen to me last week, but it was with my right analog stick; it was pointing the in-game camera toward down and to the left, in Splatoon. I tried the Recalibrate (ab+ and - buttons hold for 5 seconds) and the Re-Sync Gamepad methods, and also disconnected the right analog stick module from the main circuit board and reconnected it, but all of those methods failed.
I called Nintendo when the recalibrate and re-sync methods failed, and they were of no help. Guess what their solution was - Yep!, "recalibrate" and "re-sync". Since there was no resolution to the problem, they offered to email me a USPS mailing label, and instructions for how to mail the broken gamepad to them, and they also asked if I wanted a white or black gamepad if it couldn't be fixed...
I ended up ordering a cheap tri-wing screwdriver for $2.50 and OEM Analog Sticks with PCB Board (Left Right Set) for $6.99. I ordered from E-bay, locally, and the slowest item delivered to my mailbox in exactly 7 days from the order date.
After removing the gamepad's battery cover, the battery, and then 10 Y-shaped screws, and slowly opening and disconnecting short & tiny cable, I was onto the right analog stick replacement project. It was easy to do: removed 5 or 6 small regular screws that held down a small-sized circuit board, and then moved it over to the right and out of my way, for access to the right analog stick module (which is available to replace after taking out 2 Y-shaped screws). And lastly, disconnected the analog stick's board from the main circuit board, putting it aside, and not tossing it out, since the replacements part didn't come with thumb pad(s) or board connector wires.
Now, the fun part: I got my replacement analog stick (w/ PCB Board) and fitted it with my non-working stick's thumb pad and also it's board connector wire, screwed everything back together, and BOOM! Good to go! Booted up Splatoon, and everything worked perfectly.
The only annoying parts were that the R button and the volume control rocker jumped out from the controller casing by accident; but putting them back is (easy) but it's annoying - especially the volume control rocker.