Translation:Please call a doctor quickly!
You should write "早く（はやく）" as "quickly" regarding this situation.
”速く（はやく）” is a word related its speed.
so, between following the two sentence have a great difference although they have the same pronunciation.
we can imagine this speaker is requiring someone to start running earlier,
and this is being requiring to run faster.
so I suggest to write like this in this case,