I am getting confused about whether or not there is the accent on the final "a" in "diewczynka." In a previous sentence, I didn't put the accent and I got an "almost correct" because I did not include the accent, but in this sentence, the word is listed without the accent. I am not sure which is correct/if both is correct, and if both are correct, when should I include the accent?
By the way, it's not an accent. 'a' and 'ą' are two different letters.
I suppose the word you are looking for is 'diacritical mark' (or simply 'diacritic'), this particular one is called 'ogonek'.
They are the same word but in two different forms which depend on function of the word in a sentence. Have you read basic information about Instrumental? Look here: https://www.duolingo.com/skill/pl/Defining or here: https://en.wikibooks.org/wiki/Polish/Noun_cases#Instrumental
"dziewczynka" [Nominative] -> "dziewczynką" [Instrumental]
(ja) lubię = I like
(ty) lubisz = you like (singular)
(on/ona/ono) lubi = he/she/it likes
(my) lubimy = we like
(wy) lubicie = you like (plural)
(oni/one) lubią = they like