I am so sorry to hear about your mom. This must be so scary for all of you. However, don't assume it's cancer just yet.
It is very possible that it is an infection or something else. It could even be a scar on her lung from a previous illness, like pneumonia.
I know it seems like your mom is keeping things from you, but she's only trying to protect you. Unfortunately, if she tells the doctor to give you no information, he can't tell you anything. He could speak in hypotheticals, though, if he's sympathetic. Try phrasing it as "So in cases *similar* to this, hypothetically speaking, what are the chances it is something serious? What kinds of things could this be?" That may not work, but you could try.
The biopsy results can take as long as they take. Could be a week, could be three weeks, depending on where it's sent, how busy that place is, not always because of what they find or don't find.
Once you know more information, I would do some research on your own and make a list of questions you have and at least give them to your mother to ask the doctor, if she won't let you be there to ask yourself.
Your mom may not want you in the doctor's office, but tell her that you want to be there to support her. She shouldn't have to go through this alone. She would want to be there if it were you in this situation, wouldn't she? So ask her why she won't let you be there for her in the same way. I know you are her daughter and she feels like she needs to protect you, but you sound like you can handle this, maybe more than she gives you credit for.
The main thing is not to freak out just yet. You don't know what it is, so don't assume the worst. Please write back and let us know how things go. I wish you all the best.