Brit, do you have health insurance? If you do a walk in clinic would not be the appropriate place to go to begin a regime of medication and counseling. A walk in clinic is designed to treat immediate problems that have a quick fix (ex: cold, ear infection, stitches).
Ask your pediatrician or GYN for a rec. for a psych./counselor and new family dr. Meds are not magic pills and they are fine to take *if* you follow the program. Meds and counseling need to go hand in hand. The meds are designed to reduce the physical symptoms of stress/anxiety so you can really focus on the counseling side of things.
Do not hold off on this or make excuses. It's a matter of making a few simple phone calls and once you do find the psych/counselor they usually will get you in quickly due to the nature of the circumstance. No matter what medication they prescribe chances are it will take 6-8 weeks to reach a therapeutic level so the sooner you start the better.
I don't know where you live but I have four major hospitals in my neighborhood within a 10 block radius of each other - aside from one of them they all have mental health clinics. So if a clinic is what you choose find a mental health one.