I'm not qualified to give medical advice, but you asked for sensible advice, and mine is 'if it quacks like a duck, treat it like a duck.' It sounds like you have the current winter lurgy (there have been a few really awful bugs circulating this year which aren't Covid or flu, but make you feel very grim). Unless you develop any other symptoms, I'd treat it like a generic bad virus. You're not in any state to go out anyway, so regularly testing for Covid is a bit pointless, but if you have a stash of tests, I'd be tempted to do one in a few days, just to rule it out.
It can be scary feeling this grim and not knowing why - and adding your health anxiety to that, I'm not surprised you're having a few moments of feeling your heart racing. Tell yourself that it's only a common virus, you will get better, and try to ground yourself. I'm sure you've come across the 5-4-3-2-1 trick before given you have anxiety, but it's worth giving it a go to feel nice and calm.
5 things you can hear
5 things you can see
4 things you can touch
2 things you can smell
1 thing you can taste
I'd recommend the taste be some cough lozenges or honey water! If you don't have anything at home to help with your sore throat, your sister might be able to rummage around at her place or your parents' place and drop something over without crossing the threshold. She's not far away.
People calling you dramatic don't understand how difficult it is for you living with anxiety - I'm proud of you for recognising it in your very first post. Stopping your anxiety from rearing its head is hugely difficult, but what you can do is recognise it and call it out, and you've done that. That's massive, so well done for that.
Make sure you can have plenty of water nearby, so you don't have to haul yourself out of your bed too often. You won't want to drink loads, but the more you can, the more hydrated you'll be, and the less your throat will hurt.
Eat when you're hungry - it won't be much or often - it may take at least a few days to get your appetite back. It's fine to eat very little for that short period of time. But do force yourself to keep up your water intake, as that will help you get better.
And as has been said, get lots of rest. Sleep is incredibly healing - it's why we just want to nap whenever we're ill. Listen to body, and nourish it with plenty of water and sleep. It may be Christmas, but don't force yourself to do anything Christmassy as you're not up to it. You can see your sister and parents when you're feeling better and are less contagious. The timing is a shame, but it can't be helped - and by staying away today, you're giving your family the gift of not knowingly infecting them. That's a lovely present!
I hope you feel better tomorrow. Take care, OP.