Hi OP.
I totally empathise - I had chronic mental health problems when my son was young (particularly from 18 months - 3 years) and I constantly felt I couldn't do it alone. The majority of the time I had to, but it was a case of getting through each hour at a time until the end of the day when my ex DP came home from work. I too burdened him with things but he wasn't very supportive which made my mental health worse.
Do you have a diagnosis of anything MH wise? Have the perinatal team discharged you to general community team? I'm not sure on how long the perinatal team handle cases, as I was discharged after 3 months, but if that threshold has been met I would definitely be chasing the community mental health team for ongoing support, as well as speaking to your health visitor.
Now your baby is 1, is there any provision for getting them into childcare for a couple of days a week? It might give you a bit of a break which will allow you to discharge and wind the anxiety down - also, socialisation for young children is really good and if you are at a point where you feel unable to go to things like baby groups, will definitely make a difference.
If it's not too painful, what is it that you feel you can't do or handle? Is there anything we can help with to guide you or help you reframe your thought process to show you're doing a really good job? Put it this way, you've grown, birthed and brought up a 1 year old - you are definitely doing something right. I totally understand that really chronic sense of failure as a parent, but the likelihood is that you are wonderful, just struggling with intrusive thoughts.
My DS is now 5 and I left my ex DP last year - when my son was around 2, I was so mentally low that I thought I would never, ever be able to parent him on my own. But I am a single parent to a school aged child - I do have help from my family, but on the most part I do it alone. I still get scared of certain things and feel I can't cope, but I know it's my mental health playing tricks on me, like it's doing to you too.
Wishing you the very best 