Should i go to the doctors for a second degree burn to the finger?!

Yesterday i burnt my finger badly on a straightener. The burn has blistered and gone a purply red colour. The burn size is pretty much the whole inside of my finger. It hurts slightly to touch. I have put a band aid over it and am applying pau pau ointment to it about 2-4 times a day. It healed very slightly last night. I really dont want to have to go to the doctors. I just want to know if i should, and if my burn is dangerous or if it will just heal if i carry on treating it the way i am. Thanks :)