Am I overcoming social anxiety or not?
This may have nothing to do with social anxiety and if not then I apologize ahead of time.
I've never really been that outgoing. I do feel less introverted than I used to be. In certain situations I do feel comfortable with a few people. I'm usually not the type to speak to someone first unless it's someone I know. I don't have very many friends because I let go of people who I thought were toxic in my life plus as an adult in my 30s. We all have our own lives and we grew apart. Now I want friends but I have walls up. I don't let potential partners in let alone friends. I started a job a few months ago and I have days where I rather blend in, get my work done and go home. Other days I want to be included. It's that wall that keeps me from just letting go and talking to people etc...The wall needs to go. It would help me out so much.
Anyway, sorry to ramble.
Hello @sewest82! I can't say for sure if this is you overcoming social anxiety or something else. But despite what you call it, it is undoubtedly a change for the better and that should be celebrated! 
I'm glad that you have gotten to a point where you want to make self improvements, you are seeking more social interactions and you are comfortable asking for help. Breaking down one's walls isn't an easy thing to do. It will take time and will probably be most effective in baby steps.
If you feel uncomfortable asking if you can be included in these social gatherings with your new coworkers, it might help to simply befriend one and then get introduced to the rest of the group through your new aquaintance.
There's also nothing wrong with YOU organizing a social gathering and inviting them. If you still feel uncomfortable connecting with someone so soon, it's possible to organize a casual gathering (like getting drinks after work) and invite everyone at work. Passing around a general invite to everyone usually is less anxiety inducing than inviting a select handpicked few.
Hopefully some of these suggestions were helpful. :)
