Note: My response is probably going to be long, and will reference a few articles and sites.
There could be a number of things going on, but I would first suggest you get a squat assessment. Doubtful considering the weight you’re pushing, though it’s always good to double-check. You can get it done through a trainer at a gym, or you can get tips from an experienced member. Mean-looking powerlifters tend to be very helpful.
You can also film yourself and get critiques from another forum where people are a bit more active in this area. BB.com is poison and kids there will purposely derail threads and spread misinformation. T-Nation is better since many fitness professional contributing to the site also interact on the forums, so it creates a different culture. You can also self-assess by going through the excellent video series by Dave Tate called “So You Think You Can Squat”. It has five parts.
Now, what I suspect is the problem is inactive glutes. It is common and easily corrected. Unfortunately, there are no catch-all programs that suit everybody, so people cobble one together to address their specific weakness. Bret Contreras, The Glute Guy, has a lot of tips on activating and strengthening the gluteal muscle group, and you can use his “A Simple Test for Glute Activity” (http://bretcontreras.com/a-simple-test-for-glute-activity/) to periodically assess your progress. There are also floor version tests if your gym lacks the equipment for Contreras’. Look around the web for activation drills. Many can be used in the warm-up or cool-down portions of workouts, or performed as a supplemental program outside of main sessions.
Also look into SMR, as well as stretching your psoas muscles. The psoas are opposing muscle groups, and reciprocal inhibition can prevent the glutes from firing properly. It’s a thing, and people are likely to have shortened hip flexors due to spending a lot of time in the seated position. Speaking from experience, this will also alleviate tightness in the lower back from squats and deadlifts. (You be not be quite there yet, since you’re young.)
As for your squat depth, mobility drills can fix that. Breaking Muscle has a Squat Therapy article (http://breakingmuscle.com/mobility-recovery/squat-therapy-4-drills-that-will-improve-your-squat) with some, but I like drills in Chad Waterbury’s “5 Things You’re Missing” (http://www.t-nation.com/free_online_article/sports_body_training_performance/5_things_youre_missing). They’re fast and can be tacked to the end of intense workouts with a complementary training parameter. Also the overhead squats include thoracic extension, shoulder integrity, and allows you to focus on form. If they suit you better, the overhead can be replaced with goblet, back, or front squats.