It is very common that people feel embarrassed or uncomfortable when they exercise out in public or at a commercial gym. My very best advice is to work on adjusting your own attitude.
If you think about it what does “being embarrassed” mean? You are most likely concerned with how other people perceive you. Your best way to deal with this is to adopt an understanding that what another person is thinking should have zero effect on YOU. Their thoughts should never effect how you feel about yourself and how you act.
Do not let their thoughts control you. YOU should be in total control of yourself. This may be easier said than done but it is important to your self esteem. People definitely get into certain thought patterns that become their habits. Habits of course are hard to break. Reminding yourself that how you fell is controlled by YOU (not others) will take time and practice.
The fact that you are involved in an exercise program should help you feel better about yourself. You are engaged in a very positive activity.
I hope this answer helps you!