You are in desparate need of someone to talk to on a regular basis in order to work out your depression and to get another perspective.
There are two problems with medication treatment. One is to find the right medication, and the right leve. Once a month monitoring is okay for that.
The other problem is that medication alone is not sufficient. It has been well proven that the best approach is medication and counseling (psychotherapy). It works amazingly well. Thats what you should be getting. That's what you, or whoever is helping you, should push for.
Don't give up now. Get the right treatment, and you will be okay. If suicidal thoughts are this intense, you should get help immediately and tell them it is an emergency.
If the proper medication is found, it certainly can be sufficient treatment without psychotherapy. Practically nothing has been proven in mental health.
I believe that medication alone is almost never enough. Even if you find a good combination (took me over 10 years) there are still the residual effects that the depression or other mental illness has had on your brain. Once depressed the person "learns" more and more negative ways of thinking, more distorted thinking, and negative ways of coping. These ways of thinking can very much still be present even though the medication is working just fine. MOst people to my knowledge need the help to change these negative thoughts and coping mechanisms in addition to the medication. Without that help a recovery that most people want takes a very long time to achieve. Unfortunately it is very expensive, even with insurance to get the right amount of therapy you may need. For me that is the obstacle right now. I can only afford once a month to the psychiatrist and once a month for couples counseling. But during that counseling we both get taught new ways of coping and fighting against self defeating actions and thoughts. Take care and the best of luck.