Getting birth control in another state?

I got my first Depo shot in August when I was back home in Washington for the Summer. I attend university 5 hours away in Oregon. I'm going back to Washington this weekend, which was when I planned on receiving my next shot. Unfortunately, I realized that my clinic isn't open on Saturdays. I found this out a couple weeks ago when I was trying to schedule an appointment. So I tried to schedule an appointment with the closest clinic that was open on Saturdays, but had no luck...so I decided to make an appointment with the closest Planned Parenthood clinic (my clinic in WA is also a PP clinic). 
I'm an anxious person, so asking for a Depo shot--not only in a different clinic, but a different state-- is making me paranoid or fear that I'll be infringing on something and won't be able to get my shot on time. Have any of you had to do this before? Are there any problems with it?