Accept that you are shy. It's fine, not everyone is able to speak freely to everyone as soon as they meet them.
Accept that you do want to talk to people. It's the shyness holding you back, not other people.
Decide to over come it. Decide that you don't want this to carry on, the awkwardness is awful, the shyness is debilitating you.
Take a deep breath, start saying hello to folk. Mention the weather. Say you feel like you've not had a chance to talk to anyone yet as the start of school has been so busy.
Ask people questions, how are their kids finding school?
I have been there. I have been so incredibly shy that I've sat at parties and not said a word for hours and cringed inside at how awkward I am. I found it hard making small talk because of my shyness. I hated it.
So I leant into it. I forced myself to talk and smile and say hello. The more you do it, the easier it is.
I pushed myself - went from almost vomiting at the thought of asking a question out loud in a meeting to doing lectures and talks in front of 50 strangers and a 10 minute totally off the cuff verbal presentation with 2 hours notice in front of 350 people. I do these things because if I don't, the shyness wins and I never wanted it to win.
Accept the shyness. Accept you don't want to feel that awkwardness. Decide to push yourself and say hello to folk.
Good luck , you can do it.