Hello and welcome here. Please feel comfortable about expressing how you feel, you my find its very helpful in itself. I dont know a great deal about the Muslim culture or religion I am afraid, but most religions seem to frown upon suicide. I know you say you have a Muslim therapist, which is good, although you find you cant tell her about your suicidal thoughts. What I find interesting is, that you say 'I'm not even sure why I have suicidal thoughts'.
Even if we cant pin point a reason or cause, there is almost usually a reason for being so low, I know there is in my case. There are chemical imbalances in the brain sometimes which can go out of order and cause suicidal thoughts with o other triggers, but more often than not something which has happened to us or what is going on in our lives in the trigger.
Please feel free to open up here, if you start exploring your emotions here with those who understand about suicidal thoughts and all it brings, then you may find it then easier to approach your therapist. I think just need to take your time and no rush, you have a done a brilliant job to so far by joining the group here and for your first post, you should be proud. We are here for you, dont be afraid to ask or share.