OP I can really relate to this. I have acute social phobia. I’ve been balking at some of the suggestions on here. It’s not as simple as getting out of my comfort zone. I just physically couldn’t.
This thread has brought up unpleasant memories from my teens to present.
I did a part time access course decades ago. In my first year, nobody spoke to me. A few went as far as hello but nothing beyond that. I realised after a few months that I should have just plonked myself in the middle of everyone in the canteen instead of on the periphery pretending to read. It became impossible to infiltrate my fellow students beyond that time as firm friendships were well established by then.
All, but me and 3 others, were full time so had moved on. Thus, In my second year, I thought sod this and, learning from the previous year, threw myself right in mix as much as I was terrified. One of my biggest achievements in life (sad this to admit) is hearing that a large group met up after last lesson every Friday to go the pub. I was missing out because being p/t I wasn’t in that day. Instead of waiting for an invite that may have never come, I invited myself. I never looked back. I had a ball that year. Met fantastic friends and we socialised out of college, right through to our respective university courses. None of us were doing the same uni courses. It’s amazing thinking back how diverse our courses were. There was a tight band of us that stayed in our home city (3 universities, several campuses) and it was only when careers and families took us in different directions that that period of my life came to an end. If I hadn’t had the courage to ask which pub they went to every Friday, the following four years of my life would have been so different. I probably would have dropped out and certainly not persued with uni.
Subsequent years were spent masking my social anxiety with alcohol and drugs, I’m ashamed to admit. Being a party animal led, eventually, to a breakdown and the charade fell away. The new clean, bare and medicated me was a shock for my peers. People couldn’t accept the real me. How boring I must be! 
Recovery has involved MH groups and women’s support groups etc along the way. I’ve always thought I got on really well with the others. We even became friends on social media and still occasionally message each other. But it is so hurtful when I read in plain sight, “we must catch up soon” and the other person will say, “yes and ask X, Y and Z.” My name never gets mentioned. Sometimes on another post I may have just spoke to one of them too. In fact social media is both a blessing and a curse. This occurs with other social groups too - old school friends, work colleagues, voluntary groups and even mums from school.
I try to be kind, friendly, supportive, communicative and it’s not my personal hygiene lol, though seriously I have sat and cried. I’m anonymous.
Sorry this has totally derailed the OP but I empathise with you. I do hope you manage to arrange meeting up with the posters who have offered in your area.
To the lonely mums. I was so fortunate to live in a big city when my children were little and surestart centres hadn’t been culled. Surestart saved my life. I was going to 5 exercise classes at one point all offering crèche facilities. I do hope these will be re-introduced as soon as this lot are out. 