So I was doing the leg press at my gym last Thursday with a relatively small amount(180) compared to my max(410) and after doing only 15 reps my legs(quads) got so sore. They still feel like they're burning right now and when I walk up and down stairs I can feel the burn. Not painful in joints or bones, but the muscles feel like they're ripping out of my skin. Sure, It's good they're growing, but this doesn't usually happen. I should note however that I have been off leg work for a considerable amount of time before this happened. I am still squatting and leg pressing every other day, also. Should I continue or rest? And is this normal?
Muscle soreness is irrelevant to muscle growth. It's just a sign you haven't exercised these particular muscles recently.
Provided you've had enough rest and good calorie intake in the last few days, you are more than good to go and do the exercises. It's not a good idea to do it if you've done any intense leg exercise in the last ~72 hours.
Spend 5 min running/cycling, 5-10 min stretching before the workout, this will get the blood flowing and relieve the soreness a little bit. You may even notice your soreness has reduced after the workout.
Feeling sore is not a sure sign you are growing.
If I understand you right, you haven't been working your legs for a while before this workout (you seem to contradict yourself in the next sentence), in that case, it's normal to feel sore. Higher rep count also seem to make you more sore, at least that's true for me.