Hi,
-도 does mean 'also' when used with a noun.
However, used with a verb or an adjective, it means "even though" , "even.."
아프다 as you know is an adjective that means "hurt, painful," So the 도 here is supposed to mean "even though," so the whole thing is translated directly as
"even though I'm hurt and hurt"
and we repeat adjectives in order to emphasize the intensity, so the closest English translation for this would be
"even though I'm really hurt." or "even though it's really hurtful" depending on the subject.