In your other post you complain your GF doesn't text or see you enough and now you are not sure whether you should feel bad for not mentioning your mum's birthday?
Your relationship has MASSIVE communication issues. On top of that, you seem really scared of her, and won't talk to her coz you are afraid. Not really too healthy.
For this particular situation you could just simply apologise and say you didn't invite her coz she was sick and you didn't think she would be up to it or something like that. This situation may seem trivial but it could just be one part of a bigger problem you too are having. Maybe you are not compatible?
Some people are drains and some are radiators... Keep clear of the drains and hug the radiators!