I am so sorry you are going through this -- but you are on your way to feeling completely better soon...
The first thing you have to do is realize that the suicidal thoughts are simply a neurochemical process. We know this as an absolute certaintly because when people get on the right meds - the thoughts disppear).
So, when a suicidal thought pops into your head either imagine a STOP sign or just stop youself and remind youself that the thoughts are simply biochemical in nature and will soon go away.
You can also ask youself at that time of the thoughts coming into your head, if you really want to die, or you just want the pain and symptoms to go away - surely you have hope or else you would not have gone to the lengths of seeing a new doctor and taking the meds everyday (YAY for you!!!!! by the way).
Lastly, you can treat these thoughts as though you would treat a child who is throwing a tantrum. If you have ever been around or seen a child lying on the ground, yelling, crying -- imagine your suicidal thoughts as doing that -- and just simply tell that tantruming child that you understand - and that it will be okay - that you are the adult and you are taking care of it.
One of these should work for you (sometimes people are very visual and like the idea of imagining thoughts as children). Give all of them a try, no matter how silly they seem.
And... let me know what worked!
Is there anything else I can help with?