A Drogerie is a store that sells household goods, cosmetics, and personal hygiene items. The Apotheke sells all prescription medications, non-prescription medications, as well as non-food health products and homeopathic medicines. Homeopathic and plant-based medicines and treatments are generally more popular and widely accepted in Germany and they are strictly regulated for proper dosing and quality controls. Some common medicines, plant-based remedies and vitamins can be found for less money at grocery stores but the names are different so make sure you are familiar with the active ingredients and compare the names and dosages on the label. Please note that there are non-prescription drugs that you are accustomed to in the U.S. that are not available without a prescription in Germany. You can buy things like Ibuprofen and Clotrimizole at the Apotheke without a prescription. Mostly the names are the same but if you can't pronounce the medication name in a way that they will understand then just write it down. Many Apothekes have someone who can speak some English.
Tell the pharmacist your symptoms and they may give you medication without you having to see a doctor. The plant-based (naturopathic) products (for things like sinus congestion and such) are really wonderful. They do work and most times don't have the side effects of over-the-counter products in the U.S.