Suicidal thoughts are a symptom. Remember that. If you're having them frequently and they are bothering you, then yes, do tell the doctor. Make sure that you tell whether or not you have a plan.

I like to use the pain scale for suicidal thoughts. You know the pain scale they use like 1 is not painful up to 10 which is worst pain ever. Suicidal thoughts are not all the same. A 2 is a fleeting thought. A 10 is a "I have a plan and I've started making preparations." It's a good way judge where you are and how sever it is.