I’m 18, 5’6”, 118 lbs, size 32DD. Would I qualify for a breast reduction? (Photo)

If you mean would you qualify for insurance coverage, it is possible. Most insurance companies require that 500 grams of breast tissue need to be removed, and that usually equates to a DD cup. Also, they will want to know what you have tried to alleviate your symptoms, i.e. special bras, physical therapy, analgesics, etc. See a board certified plastic surgeon who will help you obtain pre-authorization for your surgery. Good luck.

Thank you for the question. Based on your description and pictures, you may be an excellent candidate for breast reduction surgery (even though you are starting with relatively  aesthetically pleasing breasts). This operation tends to be one of the most patient pleasing operations we perform. 
“Typical” patients who present for breast reduction surgery are women who have disproportionately large breasts, causing problems such as neck/back/shoulder discomfort, postural changes, bra strap grooving, skin irritation/rashes under the breasts, and/or difficulty with activities of daily living and/or exercise etc. There may be both physical as well as psychosocial “stress” caused by the disproportionately large breasts. Patients considering breast reduction surgery should also consider the potential downsides (risks/complications) associated with the procedure as well. Poor scarring, for example may be associated with the procedure.  Additional surgery may be necessary in the short or longer term for a multitude of reasons.
Best to seek consultation with board-certified plastic surgeons who can demonstrate significant expense achieving the types of outcomes you will be pleased with. Then it will be very important to learn about the pros/cons/risks/complications associated with breast reduction surgery. After you go through this consultation process you will be able to make an informed decision whether or not to proceed. Best wishes with your decision-making.