Relatively limited experience yields the following advice:
1. Simpson Bay Pharmacy off of Welfare Road near Zee Best. Bad advice on treatment for sunburn, unfriendly. Not recommended.
2. Pharmacie in Marigot on Rue de Republique near the corner of Rue de Hollande. Very friendly and helpful (despite language barriers) on treatment for flu-like symptoms.
3. Pharmacie de Grand Case. Also very friendly and dedicated to help (treatment for urinary tract infection, with efficient doctor's office nearby).
Bottom line: go to the French side for both helpfulness and price.