Can you post a photo of the plant? A true purple pitcher is an OUTSIDE plant. It will also need a dormant period of 3-4 months come fall.

This is it... the only problem with keeping it outside is that i live at a college and when im home there are animals that eat most of our plants

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That's a S. Purperia. It's an OUTDOOR plant and will not last long indoors. They need full Sun and winter dormancy.

I dont really have anywhere outside to put it I live in the city... would a grow light work?

I've seen it done before with multiple, bright, (like 10,000K) bulbs indoors, but you'll still have the dormancy issue to solve. If the lighting you buy works for it. Some people that live in climates not conducive to adequate dormancy conditions put it in their fridges for the 3-4 months. However, I would slowly induce a dormancy that cold. You don't have a zone number so it's hard to say what your options for that are.