Cold messages to people in my field, do they work? - first time posting

I sent 13 messages on a professional network and got two replies. It has been weighing on me all week. I worry about bothering people. How do you phrase the request?

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.

Follow up with a thank-you and a short update. One of my chats led to a referral a month later.