How Do I make up with my Best Friend?

Hey recently i got into a big fight with my friend..Well this is how it started.I have known her for past 9 months and in about 2 months we became very close friends...We chat all night and share each and everything,.What happened that we both work as intern in hospital.Nd 2 days back she got sick.she told me that she was not feeling well and i even told her to take rest and to take some med.After that i got busy in some procedure and suddenly saw that she's was not feeling well at all..Then i told her to take rest and go back home and told her that I'll drop her back home.But she refused straight away because she thought i had to leave my work to drop her.Anyways i got pissed off and went away..And didn't even cared to text her to ask about her health..After about 45 min she txd me that she was sorry for behaving so weirdly and replied her that take rest vl talk later.Later that day i didn't text her she even called me once but we had a very formal talk.Then as usual i text her that night nd then she called me.and since i was angry with her we ended up fighting and i completely forgot the fact that it was my fault coz i didn't ask about her well being in spite of the fact that we were such close friends.When she told me this i was very angry with me and said her sorry.But this didn't work.and it was in this conversation she told me that i was her closest friend and at least i should have cared...Now she's become very formal with me..What should i do to get back my best friend back.