Having parents with bipolar disorder and depression leave you quite genetically pre-dispositioned to develop mental illness yourself. However, simply experiencing bouts of sadness occasionally is a normal part of daily living. The concerning factor is that this sadness has manifested into suicidal ideation.
You could do very well for yourself if you started to keep a journal of these moments. When you feel this sadness, take down the date and time, and then write down what is going on... Where are you, what has happened today, what are you anticipating, what thoughts are in your head... This journal will prove invaluable when going to a psychologist for assessment. They may be able to see patterns in your emotions that you cannot easily see yourself, and be able to address whether or not they are indicative of true mental illness, or simple episodic sadness or depression.
You are in the middle of puberty, and it is entirely possible that your hormonal levels are changing right now.
One thing I wanted to say is, sometimes what people perceive as a "sinking feeling" in the chest or sudden sadness is actually a biological response to anxiety. Many believe that suffering from anxiety means that you will feel nervous all the time, but the reality of anxiety disorders is that they manifest in many different ways. It can be from systemic depression like the sinking feeling in your chest, all the way to digestive issues, headaches, body pain, insomnia, frightening dreams and more. You should make sure to journal any abnormal symptoms you experience.
Just know that while it raises your chances of developing a mental illness, having mentally ill parents does not guarantee that you will be as well. Asking for help to figure it out is not "dooming" yourself to a diagnosis or to taking medications. Getting assistance in understanding your emotions and body responses to those emotions can really help you cognitively manage your feelings, so that you do not find yourself getting swallowed up. It also enables you to have someone on your side, if your symptoms start getting completely out of control and you need to be more aggressive with treatment.