A word to describe someone who is bad at handling their emotions? [closed]

As one of the comments mentioned, volatile suggests this idea of "ready to explode" at any point.

If someone is volatile, their mood often changes quickly.

"He accompanied the volatile actress to Hollywood the following year."

"He has a volatile temper."

This can convey both positive and negative emotions, and the person flipping between them quite quickly.

Another way you could describe them is "bottling up emotions". This implies that they bury their emotions as you said, rather than dealing with them, but also conveys that at some point the bottle breaks and they react very strongly.

I'd like to suggest the word touchy.

Touchy: https://en.oxforddictionaries.com/definition/touchy

Meaning: Easily upset or offended; oversensitive.

Usage: "she's a little touchy about her age".

There are two terms I have, "maladjusted" and "labile". Both are psychological terms. "maladjusted" is mainstream, "labile" not so much.

labile
adj.
1.1 Of or characterized by emotions which are easily aroused, freely expressed, and tend to alter quickly and spontaneously.
‘mood seemed generally appropriate, but the patient was often labile’
Oxford Living Dictionaries

Emotional lability

The person experiencing emotional lability usually feels like they do not have control over the emotions.

and

maladjusted
adj.
2. Inadequately adjusted to the demands or stresses of daily living.
American Heritage Dictionary

adj. Failing to cope with the demands of a normal social environment.
Oxford Living Dictionaries