Not sure what the exact issue was with exporting but did you use Swivel? It converts swf's into mp4's and it's free! It's developed by Newgrounds and it's definitely the best converter for swf's to mp4's out there: https://www.newgrounds.com/wiki/creator-resources/animation-resources/swivel-flash-to-video
For your first Flash cartoon, it's super cool! Hope you can do more with the program and get used to its quirks!
EDIT: Didn't even realize newer versions of Flash let you export natively? Anyways, if the media encoder is being a big piece of shit like that, just export the file as a swf (you can do this quickly using ctrl-enter) and plug it into Swivel from there. If you need help with audio sounding like crap in the swf or anything, just PM me!