I sprained my ankle 3 months ago, still swollen and it is tender around my talar dome/fibula. Is it a possible ligament tear?

Good Guess. Anything is possible. Your ankle needs to evaluated both physically and with imagery. See a professional.
Yes. An ultrasound would show any ligament tear or rupture. MRI would show a talar dome injury. Start with an x-ray and evaluation by a Podiatrist. Ice will help with swelling and an ankle brace will help with stability.