Hmmmm. I had to medicate our miniature schnauzer with metacam for arthritis for a long time, and I remember the syringe being quite large.
A friend of mine had to medicate her rat with metacam, and he wasn't even close to a pound so there is a way to precisely measure the amount. I had to medicate our rat with children's liquid advil, and the syringe it came with was tiny but it still wasn't precise enough to measure the correct amount. My friend gave me one of her 1.0 mg/ml syringes, and that worked perfectly. Is there an emergency or after hours vet from that clinic you could get a hold of? Did the vet tell you to medicate by drop?