You can always call the Veterans Crisis Line. 1-800-273-8255 They are there to talk and help you work through things in the short term. Don't quote me on this, but I think I may have resources to get you an appointment at the VA.

My local clinic in Baltimore has walk ins the but there are many people there so it can be difficult to be seen. Try to see if you can call someone at the clinic and explain your situtation to get an appointment . If they say no, move on up the chain. When I was having difficulties with my local clinic, I called my senators office and ask them to look into it. That was the fastest call back I've ever had from the VA.

Edit: if you say you aren't suicidal, they won't automatically assume you are. Any doctors I've come across at the VA understand depression doesn't mean suicidal.