ANSWER: Easton's Bible Dictionary states that the 'Sharon' in the term 'Rose of Sharon' was a level tract or plain that ran from Israel's Mediterranean Sea coast inland about 10 miles and which was roughly 51 miles long (running from modern Haifa in the north to near Tel Aviv in the south). The area was well-known for its beauty and fertility (1Chronicles 27:29; Isaiah 33:9; 35:2; 65:10). The flower is celebrated in the Song of Solomon. It is called Lasharon in Joshua 12:18.
The Song of Solomon uses this flower to describe the beauty of a young woman (2:1). The plain where the flower was found was known for its beautiful flowers in the time of Solomon. The entire second chapter of the Song of Solomon is quite poetic.
1 I am only a wild flower (Rose) in Sharon, a lily in a mountain valley. 2 Like a lily among thorns is my darling among women . . .
Come then, my love; my darling, come with me. 14 You are like a dove that hides in the crevice of a rock. Let me see your lovely face and hear your enchanting voice. (Song of Solomon 2:1 - 2, 10, 14)
No one today knows exactly what this flower looked like at the time of Solomon. In the first verse of the Song of Solomon (sometimes referred to as the Song of Songs) chapter 2, the Hebrew word chabatstseleth (Strong's Concordance #H2261) is translated as our English word "rose."
According to one commentary, many authorities agree that the flower mentioned by Solomon was some kind of bulb plant. Some Hebrew lexicons say this word is referring to a meadow saffron, many of which can still be found in the area today. In any case, there seems to be no reason why the rose, of which several varieties are common in Palestine, should not be meant by Solomon.
Gilead, part of ancient Israel's inheritance from God, gave its name to the balm of Gilead mentioned in the Bible (Genesis 37:25, Jeremiah 8:22, 46:11) as a healing ointment of great value, sometimes used as a trading commodity. There is no direct Biblical connection between the balm and the Rose of Sharon, but your question regarding any medicinal use of the plant was quite interesting since portions of today's roses are used for medical treatment.
The Bible does not use the rose as a symbol for Jesus but this phrase obviously has had tremendous resonance in modern culture.