disciplining problems

A while back ago someone said (not to my face by the way) that Liam is "too aggressive" and it's because I don't discipline him. 

 I'm very upfront about Liam's biting/hitting issues with everyone we come in contact with, especially if our children will be playing together. I never let an incident pass without addressing it and I let the other parent know they shouldn't be shy about telling Liam "no," etc. I've read several articles about the topic. I have asked other moms for advice on what to do. When we are out in public with several children present I watch Liam like a hawk, making sure he doesn't do anything he shouldn't. Believe me, I am thoroughly embarrassed when an incident occurs. I feel like a horrible failing mother. I am also extremely grateful when other parents are kind, understanding, and patient with my boy. I really don't think Liam's intention is to harm. Most of the time he just gets overly excited and doesn't know how to express it. 

So yes, it's a problem. And I'm doing my best to correct it. I can understand if you don't want your kid playing with my kid. I can understand if you're upset because my kid made your kid cry. I will say that being a parent is not easy and that not all kids are the same, and that we could all do without the mom and kid bashing. I try really hard not to judge other moms and kids because I know we're all trying our best. No one wants their kid to be a biter or hitter. 
So if anyone out there has any helpful advice or tips with how to deal with this, then I am all ears! I'm at my wit's end over here. Sometimes when Liam hurts another child I just want to cry because I'm so upset and embarrassed. And if you think I am making some kind of a mistake then please address me kindly. Thanks everyone.