ESA income-support 6k savings limit

Hello please advise me I'm so scared, I'm on PIP and ESA income-support. I thought that the person claiming ESA income-support benefit cannot have savings over 6,000 and I didn't until I got back pay from PIP (about £2000) two day ago, so I looked online because I knew that my balance went slightly over £6000 by £600 so i would have to pay back some money, however I saw online that the whole household's savings cannot be over 6,000 when claiming ESA income-support is this true? I live with my mum and she is on Universal Credit, not on any ESA or LCWRA. It always says online that while claiming Universal Credit YOUR AND/OR YOUR PARTNERS savings cannot be over £6,000 but we are not partners she is my mum, I alway assumed that it was the same for ESA income-support, however after seeing online today that the whole household's savings cannot be over £6,000 I'm so confused and scared. So anyway after seeing this online I asked my mum to help me count all our money together and it comes to a little over £10,000 and it's been around this amount (sometimes £8,000 , £9,000 etc. depends on what's bought) The point being is that it's been over £6,000 For about 1 year and few months. I'm so so scared I had no idea I really thought it was 6,000 per person that was claiming unless it's a couple, what do I do? I'm so scared will she also have to pay back Universal Credit? Is Universal Credit also £6,000 per household or per partners? I'm so confused and scared.

Thank you so much for reading and replying. Also few things that I forgot to mention;- not sure if they are relevant/important but in case they are: I'm 22 years old. Even though we have separate incomes I from ESA and PIP and my mum from work and UC since we live together we split our expenses we both pay for rent, heat, food etc. Also this information I think may be important:- since I don't leave my house due to PTSD my ESA goes in to my mums bank account and then she take this money and her money and pays for things, do you think dose things change anything in regard not having to worry?
Thanks

Thank you so much for reading and replying. Also few things that I forgot to mention I'm not sure if they are relevant/important but just in case they are;- I'm 22 years old. Even though we have separate incomes I from ESA and PIP and my mum from work and UC since we live together we split our expenses we both pay for rent, food, heating etc. Next I think this may be important;- due to my PTSD I don't leave the house so my ESA is paid into my mum's bank account and then she takes that money and her money and pays for the things mentioned above. Does this change anything should I still not worry?
Thank you

This is the third time I'm writing this so sorry if you get three replies from me that are the same but it's just not showing up for some reason.

Thank you so much for reading and replying. Also few things that I forgot to mention I'm not sure if they are relevant/important but just in case they are;-we live in Scotland, I'm 22 years old. Even though we have separate incomes I from ESA and PIP and my mum from work and UC since we live together we split our expenses we both pay for rent, food, heating etc. Next I think this may be important;- due to my PTSD I don't leave the house so my ESA is paid into my mum's bank account and then she takes that money and her money and she pays for the things mentioned above. Does this change anything should I still not worry?
Thank you

This is the third time I'm writing this reply so sorry if you get three of the same replys from me but it's not showing up for some reason.

Thank you so much for reading and replying. Also few things that I forgot to mention I'm not sure if they are relevant/important but just in case they are;- we live in scotland, I'm 22 years old. Even though we have separate incomes I from ESA and PIP and my mum from work and UC since we live together we split our expenses we both pay for rent, food, heating etc. Next I think this may be important;- due to my PTSD I don't leave the house so my ESA is paid into my mum's bank account and then she takes that money and her money and pays for the things mentioned above. Does this change anything should I still not worry?
Thank you