I think it's okay to keep it at that size as long as you fill in the black bars, they are quite ugly.
Also, on the image itself the colours aren't very good, the tones are very similar and end up making somewhat of a gradient effect, this never looks good on pixel art and they
are very dull colours the fluorescent blue, muddy orange etc. I suggest looking at the colours Pixel used or even colour palettes from other games, there is nothing wrong with
borrowing a good palette.
Another thing is something done quite often in pixel art called jaggies, this is where your lines are jagged and create a rough looking effect. An example being the right side of
the jaw, it goes 7px, 3px ,3px, 8px making the jagged effect. A smooth transition on the jaw should be something like 6px, 4px, 3px, 2px, 2px, 1px, 1px, 1px, 1px. This gives the curve
a nice gradual effect.
Also there is little contrast, an important part of pixel art is contrast it is what makes a good pixel art pop. Another word for contrast would be values and a good way of checking values
is by occasionally making the image greyscale. Currently if you do that you can see that the hair and face have very similar values meaning that the image looks flat, here is an example
look at the Kazuma picture it looks normal and is well defined even if you put it in greyscale, this means the image is not relying on the colours to differentiate the different parts (hair, face etc) it is
instead relying on the contrast.
From a character design point I think you need to add a nose or a slight indication of a nose, because prior to reading the text it was quite hard to tell whether it was a scarf covering the face or just
the top of some sort of robe the character was wearing.
Finally the line work on your image is quite thick and visible, notice on the Kazuma picture there is no real line work, this makes the face nicer to look at and makes it seem more soft and
flowing, like a human face would be.
I hope this helps , good luck!