how to restore shiny look after painting

Recently I have fixed a bump on the rear side of my 330i
in a cheap body shop in Tijuana, Mexico.
They primed and pained that bump relatively well, but the problem is in
not shiny surface of the pained part and I can feel some tiny unevenness
on the surface.
I'd like to restore glossy look of the painted part.
What would be the recommendations?
Do it by myself?
If so, what steps do I need to take -parts, materials, etc.
Any web links would be appreciated.
Or tale my car to a professional facility. What facility? How
much it could cost.
I'd like to avoid unreasonable expenses, if possible.
TIA.

hi mate you will need to fine sand and buff I have my own body shop in the
uk, Check my site at www.freewebs.com/dannyd1110
Uk spec of the products are 1500 - 2000 grit sand paper, g3 cutting paste,
and a buffer with a compound head, All you do is flat carefully with your
sandpaper using water this wil ensure your paintwork is smoothdry off
yuraim is to get all imperfections out including any orange peel! repeat
if necessary, add some g3 to your buffer then compound the required area,
wipe off with a soft cloth, polish and voila, email me from my site if you
need any further assistance and will you please check my links as they earn
me cash, thanks mate