I don't know much about mood stabilizers, I've only ever been given anti depressants and they don't work at all. I might look into them and mention it to my Dr. I'm in the UK and mental health support is soo bad, so it's hard to get help with anything.
Go to your doctor ASAP and urgently and explain you are having extreme suicidal impulses and mood swings, and that you need to be referred to a psychiatrist because you are afraid of what action you might take. You have to insist on seeing a psychiatrist and getting a diagnosis. Don't downplay how ill you - be direct and honest about it.
I was really surprised, when I did that (because my colleagues literally forced me to, because they are so worried about me), that I have an appointment with a psychiatrist within a month. Which is really fast. I told them how suicidal I am feeling. I am still surprised about how fast it is. I expected a 4 month wait. It might be longer for you, but the sooner you get on the list, the sooner you will be seen.
Another option that a very unwell acquaintance of mine did - is to go to A&E and make a very big fuss and insist your need is urgent. Apparently this can get you bumped up the waiting list.
Definitely insist on seeing a psychiatrist and get a diagnosis and other medication. You will want to try Lamictal probably which is a mood stabliser and can work wonders for people. Another option could be Lithium Carbonate. Why not give yourself a chance at a happier, more stable life (when I say that, I am lecturing myself, as every day is torture and I really want it over - and I have an NHS psych booked for beginning of April).
I'm always telling myself my mental illness is not as bad as some - but I am wishing for death every moment of every day unless I am on drugs. So it is pretty bad. We need to get ourselves on the waiting list. Please do...