When it comes to medication, sometimes it is necessary to use small amounts of animal products because that is how they are made. It doesn't make you any less of a vegetarian. More medications than not involve animal products or animal testing in some way, and unfortunately it's hard to avoid. If your doctor wanted you on Prozac v. any of the other antidepressants, it is probably for a reason. Discuss your concerns with your doctor, but we are not qualified to tell you what a better antidepressant for your condition would be.
Prozac is available in liquid though, if you'd rather drink it than take it in a capsule. I can't say how widely available it is though, or whether it is covered by insurance, or more expensive.