First off, welcome to PC! I'm so happy you found our community!!
I had a very similar issue with my anxiety, so I can totally relate. Are you presently seeing a therapist, because I would highly recommend seeking help to discuss your past fears/anxiety and your present worries for your son. I think he/she will be ale to guide you best and help you to work out the best way to handle these situations, as well as grow + help you get to a place where you feel like you can set a good example for your son. Likewise, since you said that your mom and grandma both suffered from anxiety, it is entirely possible that it's in your son's genes to inherit an anxiety disorder (and it's entirely possible that it skipped over him too)!
I think it would be in your best interests to work through and improve your social anxiety, so that you can live in happiness and confidence. Once you get to a solid, healthy place, you will be able to set a great example for your son. You are making great strides just by seeking out help here, identifying your goals of wanting to help yourself + your son, and working on staying positive and decreasing your worrying. You are going to do great!! It's great that you want to improve your health, and your son is definitely lucky to have a great mom like you.
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Never forget how loved and beautiful you are!!!