I agree that it would be good to tell your meds prescriber about these thoughts to see if they want to change your meds.
You are not alone, though. I have read many posts on this forum from people who struggle with the same problem. I did myself for years. At the moment, I'm almost completely free of suicidal thoughts. They went away after a therapy session. I'll talk more about that in a minute.
I don't know how long you've been dealing with episodes of depression. I had constant thoughts of suicide during the first episode I had.
I have been dealing with depression now for over 20 years and I found that eventually, even when my depression was lighter, the thoughts of suicide didn't go away. They were less urgent - just always there in the background, as if to remind me "If it gets too bad, this is a way out."
The thoughts became less alarming over time but I was never comfortable with them. They were a constant source of distress.
The therapy session that helped them to quieten down was one where my therapist asked me to try to identify the part of me that the thoughts were coming from. This is something that you have to sit quietly and be sort of meditative to do.
I found that I
was able to pinpoint a part of me that seemed to be generating these thoughts. I asked that part what it was trying to do for me. The answer seemed to be that it wanted to help me to know that when I felt really depressed that there was this way out for me.
I also found that when I would get upset about something, when the thought that "If it gets too bad, you can always kill yourself" popped into my head, it would distract me from whatever was upsetting me, because then I would be upset that I was thinking about suicide. (If that sounds really convoluted, it is.)
Since I sort of realized what was going on, the thoughts of suicide have gone almost completely. I might think of it once a month instead of everyday.
I don't know if this story will be of any help to you, since I think that during very bad depressive episodes, thoughts of suicide seem to be an actual symptom of the episode. I think I've read that they can actually be linked to physiological states in the brain.
You might do a search for foods that help mood (and supplements too) and try adding those to your diet. Some people are more sensitive to the effect of foods on their mood than others, I think.
I hope you find an answer. Constant thoughts of suicide are alarming and stressful.