Are humans obligated to better themselves and will that make them happier?

Obligated, no...but I believe it does increase happiness.

Its human nature to want to 'better' yourself, unfortunately it doesn't always manifest in the same way nor do people go about it in the same way.
There is a point where I think bettering yourself becomes pointless to you personally.

Idk about obligated, but surely, improving one's emotional health or lifestyle cant hurt!

“Better” is surprisingly subjective.