Very important to get in the good habit of doing a warm up before an efforts (non coached) session, a tempo run or a race. A good warm up will increase your heart rate and the blood flow, allowing more oxygen to reach your muscles.
It will also activate the connection between your nerves and muscles which improve your efficiency. The dynamic stretches will activate the muscles and and improve your range of motion.
It will also prepare your mentally for the challenge ahead. The warm up is also a good opportunity to do some drills which over time will improve your running form.
I’m aware we can feel self conscious especially in a race environment where 90% of people are standing around chatting. But I’ve found the result of people looking over is they soon start to copy what you are doing. So in fact you’re inspiring others to warm up properly.