I am 16, sexually active, and have been on birth control for about 4 months now. I was told that if you skip your placebo pills at the end of your pack you won't get a period so one month I did this and my period started anyway. I had already skipped the placebos and continued to take birth control so even though I had already started my period I continued to take them to keep me regular, my period went as normal (besides the fact that it was still going when I was still taking the pill) and after it was supposed to be done I started to get this thick brown discharge. I started my period August 16th and my period usually lasts for about 5 to 6 days so it should have been finished August 21st of the 22nd but once the bleeding stopped the thick brown discharge came and has not gone away and its been a over a week later, and I'm starting to get worried.
I've heard this discharge is normal but for it to be going on for this long and for the amount to be this substantial is unsettling.
Any help at all would be extremely appreciated.

Only being on the pill for 4 months is a VERY short amount of time and your body is still adjusting to it (So backup birth control is HIGHLY recommended for at least 6 months).

Skipping your placebo CAN allow you to skip a period, but since your body hasn't adjusted yet, that would probably explain what you experienced. It can stop a period - but its not fool proof.