Hi, welcome to the community!
Check out this thread
on starting a petite wardrobe on a budget - I inquired about it a couple years ago when I was nineteen and starting out in the workplace.
I'm shorter, but heavier than you - Try H&M for tops and skirts. I've found that H&M things run really small, especially in the waist - I'm full-waisted for my size, and often I have difficulty buttoning up my blazers from there. You're about 14lbs lighter than me though, so I don't think you'll have this problem. Pencil skirts hit about an inch above my knee.
If you're Canadian, I highly urge you to check out Aritzia (they also have a few U.S. locations). My friend is a good half a head shorter than me, and under 80lbs and she gets almost everything there. They are on the pricey side ($60 for a dress shirt, $125 for a blazer, $55 for shorts), but they do run extremely tiny - EVERYTHING they sell goes down to a XXS (Or XXXS I've heard and seen a couple times?) and 00. Their Talula Exster shrunken blazer in 00 has ~13" shoulders and hit at a good length on a smaller frame. It retails for $125, but will occasionally go on sale for slightly cheaper. They also have very beautiful 100% silk items in their T. Babalon and Wilfrid lines, but they're a little outside my price range ($100+). (Note: Their pants have pretty high rises and may not work - They were all MISSes for me, but i'm 4ft11.)