I sprained my ankle three months ago, but it's still painful and very noticeably swollen. Should I be worried?

Unstable. Pain and swelling, after three months, demonstrates that your ankle has been left unstable by the sprain. You are experiencing, your bodies way of treating, the instability. You need to have a thorough evaluation, with imaging studies, to appreciate the extent of the damage. In the meantime, RICE and supportive measures need to be taken.
Ankle sprain. Persistent swelling of any injured limb is not normal . Try RICE plus 2 weeks of alleve , 500mg 2x a day . Avoid actitivi ties which cause more pain or swelling , . Consider a virtual consult if this is not helpful .
Proper treatment. Healing time depends on treatment you received & the severity of the sprain... (what ligaments were actually injured). You want to make sure you had adequate time splinted &off-loaded for proper ligament healing to occur. Even with the correct treatment time there can be other factors involved such as cartilage damage and or tendon injury..check with your physician for continued care.