Aahhh… Dude with the cool steampunk 
First of all, kudos for taking the leap and ‘exposing yourself’ in public 
Bravo
Congratulations
and well done!
There, that wasn’t too hard, was it? 
Not only do you earn positive vibes for your efforts, and learn something by simply doing it, but hopefully others will chip in and give you further food for thought as to how to improve even more.
Here are my 2 cents:
As Michael points out, singing whilst playing can be tricky, and something sounded ‘off’ to me 
I believe you are making a rookie mistake, which I have made many times, and I’m surprised folk don’t mention more often here.
Starting to sing on the wrong note 
You are playing the song in E minor. The Tears for Fears original is, I believe, in F# minor (same chords, but with capo on 2nd fret). The Gary Jules version is (in between) in F minor, capo on 1st fret.
If we just work with the E minor key you’re playing in:
I believe you start singing the note B, whereas the original starts on the root note E.
In the chorus I find it kind of funny, the ‘funny’ should besung on C# (I think you’re singing an A).
Essentially, I believe you’re kind of singing harmonies, which makes it sound odd to these ears.
I would suggest putting a capo on the first fret and singing along to the Gary Jules version, as it’s simpler and slower, and just focus on singing the same notes that you hear.
Hopefully this makes some sense (and is not all codswallop!)
In any case, well done again.
Give yourself a pat on the back 
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