Some of the replies are really lacking in understanding.
I fully accept for society at large, there's not a significant amount of judgment associated with being a single mother. (Note: I said 'mother' and 'not a significant', as I don't believe it's entirely gone, sadly).
However, for individuals, and some localities / backgrounds, it can be different.
OP, your post resonates with me (single parent to 3 DC, abusive ex). I also had such shame, guilt & isolation around my status as a single parent.
Like you, those feelings were grounded in childhood, and the expectations in my family. These can be very deep-rooted.
Also, I live in a particularly homogenous world! A well-off suburb in Dublin as it happens! There are a few other separated parents in my circle, but they are few. Most couples are well-off, close to family, professionally educated & lacking in any kind of understanding of what I face.
For several years, I rarely disclosed my situation. I never discuss it in work (that's not necessarily about shame, just privacy and not wanting to open up in that way). Sometimes I simply couldn't; sometimes I knew I'd get the head tilt & no understanding of what my life was like.
I have had a lot of therapy / counselling & so much has changed for me, and how I view myself.
I think I'll never not have sadness & feel some responsibility about the poor choices I made, but also treat myself with kindness & recognise I have done, and continue to do, the best I can.
You are very fortunate to have close friends - I have no-one at all I can confide in, including family. (Despite knowing many people casually). For a long time, this feeling of loneliness ate at me. But I feel much more at ease with myself now, I've just finalised my divorce, after a decade & feel there's a future ahead for me.
So OP, I get you. Your feelings are valid. But now it's time for therapy to help you through. It will be better. Not easily or quickly, but you'll get there. 💕