Your sentence makes sense, but it does not seem the best of English. Since you want to communicate about the steps you would take if such a situation happens to you today, you should not use "supposing that I have this...." because this sounds like you already have that situation rather than you coming across one. Also, on my own doesn't seem natural when used at the end of the sentence. Also, "my decision" is a better way to communicate the same idea. A better made sentence would be
"Suppose I come across such a situation today, I would first listen to what my parents say and only after that would I make (or take) my decision."