I believe I have torn tendons in my ankle but im a huge basketball player. Should I get it checked out before I continue playing or will I be ok?

Yed. Recurtrnt instabilty with easy to turn ankles result of no treament anf playing befote healong why do you think thr pros are out with ankle surgery.
Ankle sprain. Ankle swelling, pain at each step? Tendon damaged and may totally rupture if not rested and treated properly. Sprained tendon ends up healing longer than it should be, making the ankle less "tight" and be loosened, facilitating more sprains and even more loosening of the joint till you can barely just walk, and no sports for life. You like that kind of life? Not self treat most important joint.
Yes. Do not play basketball with injury?That could make the injury worse. Check out, other if the injury got bad you not able to play agian.