Hey there,
I know how you feel and i can relate to what you said in your post you're not alone *cuddles*
Seeing a psych would help you get to the roots of you're SI ( Does your psych know about you SI?) and once you knew the roots of it you can work on solving it,it takes time i needs loads of efforts but you can do it , SI has many underlying issues,it's not the main one...
Medication would help you deal with you're depression and may be you're suicidal thoughts which may help you decrease the times you SI i think.
There are very helpful articles about SI on RYL main site may be if you read some of them it may help you deal with your SI , see the
link stay strong and be safe xxx