Welcome to YT
It sounds like your silky got himself all over-excited from playing with your neighbours terrier and that excitement spilled over when he saw the lady and child. I agree that some training classes might be a good idea....if this is the first time he has been aggressive it would be a good idea to 'nip it in the bud' (if you pardon the pun!), before it escalates.
I can't advise whether or not having him neutered will help aggression issues as I had mine neutered at 6 months......but I know a lot of people say that it does help.
Good luck with him
xxx