I bet your cousin is a bit exasperated with hearing all about what Nellie said and Nellie did, blah, blah, - and a bit of irritation escaped.
It’s not your fault at all but I’d cut her a bit of slack.
It’s a really common for some elderly people to not-so-subtlety big up x’s contribution to y, to show y firstly how x values them, and secondly as a model of all the things y could be doing better.
My mum does this now she’s in her 80’s about key “friends” - who are mostly paid carers or help. All I get is “Debbie is so thoughtful”... “Oh! I stopped taken them because Debbie looked up the side effects and ...” ..., “I’m so lucky to have Debbie nearby”.
It’s not Debbie’s fault - well except I wish she’d keep her medicines-are-poison conspiracy theories to herself.
I bet Aunt is constantly regaling cousin with “Well I asked Nellie and SHE said...”
All mums friends know she does this and they all know how much I do for her, which she seems to resent strangely. It’s just a foible. She will tell them she never sees me, but they see me parked there themselves so luckily they know it isn’t true.
It sounds like you are really very helpful to your Aunt, I’m very grateful my mum has her friends too. It doesn’t mean I don’t allow myself the odd eye-roll or private vent with my daughter after another round of listening to their virtues and opinions.
I agree with other posters, it could be helpful to keep in regular loose contact with cousin and keep her in touch of anything official you’ve helped her mum with. Also take what she says about cousin not helping her with things with a pinch of salt. She may or may not, or her mum might not want her too and block her. Funnily enough, one of mum’s favourite friends told me they’d had similar with her mum before she died; she had them all running around telling them she never saw anybody from Monday to Sunday but she’d find her brother had been twice that week, and then chatting to the lady at the day centre that her mum had been in for her lunch three days etc... Similarly her brother wasn’t told about his sister’s visits
Mum’s friends regularly text me which is very helpful as I am 50 minutes drive away and she can deteriorate quickly when ill.