OO, while the nursery worker went about it the wrong way, she is not diagnosing your child, she is saying that in her experience your child is showing some behaviours which are causing concern.
When you work with kids every day, these things do stand out. You might be able to make an educated guess at what it is, but that is for the professionals, but you do know something is wrong.
There sound like a few things are cause for concern here, and your dds behaviour may be related to the lack of structure and careat nursery, or related to her own needs, but either way, she is not happy there.
She is only 2. The natural environment for a 2 year old is in a domestiv setting surrounded by familiar people, a few adults, knwon well. Very few nurseries are able to provide this. Some 2 year old take this in their stride, some don't. Your dd doesn't even have a key worker at the moment!
She behaves differently because a as an environment it is very different. Biting is a form of communication. She can;t speak, (this is also a cause for concern if she has no noises/babbling pre-words at all) so she expresses need and frustration by biting the person in her way.
I would not wait for SALT. It may take ages, and then may not give you as much as you need.
I would also try and teach her some simple signs to support her communication, and look up all the pre speech activities to assess where her communication is (things like does she understand simple instructions, does she show you things, does she point etc)