I'd expect both pharmacies to stock needles and syringes, but if unavailable, I recommend going to Chula MD Pharmacy near Sala Daeng BTS. They will have everything you need. If you visit, you might also check if they stock Testoviron depot as their prices are generally lower than any other pharmacy.
I recommend using 3ml syringes with a 18G 1 1/2" needle for drawing, and 25G 1" for injecting.