Hi ChocolateCello! Welcome to the forum.

I've been in sort of the same situation as yourself - I've done co-operative education high school (unpaid), and I'm now in the co-operative education program at my university (paid), so I've certainly had experience in shopping for petite work attire on a budget. When I was first starting off, I created a similar thread asking for help. I suggest you read it if you haven't already.
starting-a-petite-work-wardrobe-t120.htmlI'm 4ft 11, and my stats are 28-24-30, so you have a smaller waist and larger hips than myself.
While I've had some luck in the childrens' department, I tend to stick to cardigans when I'm looking there - I have this one cardigan in a children's size SMALL. Kids cardigans can be worn for a "shrunken" fit and be passable, but stick to simpler designs with more sophisticated details - Avoid cheap looking buttons, etc. I don't think you're going to have too much luck looking for pants or skirts in kids wear - My 30inch hips no longer fit.
I've had the most luck shopping at H&M. Their size 2 is pretty tiny. When shopping for tops here, my experiences are as follows:
1. Too roomy in the bust
2. Waist is snug
3. Too roomy in the hips
4. Armholes are too big
Since you're taller, waist is smaller than mine and hips are larger, I think you'll have luck in H&M as well. My
favourite spring blazer is from there - Click for my review. I've also success with dresses and pencil skirts from H&M. H&M pencil skirts tend to hit right at/above the knee for me, so they should be of an appropriate length on you. I have never tried on a pair of pants which fit from H&M.
When you're shopping for pants, look for a "skinny" cut - Skinny pants tend to run smaller, and the bunching at the ankle it sort of cute, especially with shoes - This saves you money in hemming. I've found both BR and AT petite pants to be WAY too big on me - Huge waist gaps. Personally, I've found it much easier to find a skirt that fit, versus finding pants.
I would spend a week or two in the work place before spending too much money on a new wardrobe. You'll often find that the actual clothing worn by employees are more relaxed than the official dress code. Last summer, my job required "business professional", but in actuality, everyone wore polos, khakis, sleeveless tops and Bermuda shorts. Personally, I feel the need to dress up a tiny bit more, even if other employees are more casually, to look older and be taken more seriously. I feel I'm often treated as a child by some in the work place because I look very young.
I hope this helped; congratulations and best of luck in your internship!