it might be worthwhile going to the GP to see if you could get counselling or something, as it sounds like there are things in your life that are causing you to be anxious.
People are often prone to blame behaviour that they don't like- e.g. someone being grumpy on something being 'wrong' with the person e.g. your mum thinking your depressed, rather than just fed up of having her around all the time!
It's important to remember than any mental illness is part of a continuum of what is normal. Imagine a line going from manic to depressed with hypomanic, happy, indifferent, low mood, depressed, severely depressed. most people will be roughly in the middle, less as you go towards the far ends of the scale. Those with a diagnosed mental illness tend to be at the far ends of the scale. It's normal to get some symptoms of depression/anxiety and still be 'normal'. It's whether it is having a detrimental impact on your everyday life and preventing you from doing what you want or need to do that requires thinking about. As if your mum is suggesting that you are depressed that is kind of suggesting you need medication…but of course medication comes with side effects so it's whether you think you would rather have your symptoms or the side effects. Hence why I suggested that if you are able to get on with your everyday life, and feel surprised at what your mum is suggesting, counselling might be more beneficial!
FWIW when I'm properly depressed I find it difficult to do anything due to my brain just being filled with fog and thoughts of death. Tidying, washing up, looking after the children- I just can't do it. I'm 'better' now in that I can function but still think of death on a daily basis/end up in tears in inappropriate situations on a daily basis!
When I've been said to be anxious to the point that it's a problem I've been continually jittery, having very frequent panic attacks/not able to eat due to feeling sick due to feeling anxious/having to keep moving/catastrophising/still no concentration. So they are quite different, looking at it written down. But these feelings were generally all day, and draining.
It sounds like you have reasons to be anxious- relationships etc- do you think talking about it with someone might help?