What should I do about my living situation?

I am 20F living at home with my mom, 41F, and my little brother, 18M. I was SA'd by my little brother a few years ago (about 3), and have only come to terms with it recently. I had only told a close friend just 2 months ago. I have been feeling disgusted with myself, as well as pent up resentment and so much anger towards him. Last week, I finally had the courage to tell my mom. I prefaced it by saying "just know I am telling 100% of the honest truth. you need to believe every single word I tell you", and she agreed. She then asked my little brother about it right after: I was listening in on the conversation in my room. He denied it, got angry, came to my room door, hit it hard a few times, and said "stop lying and saying things that I never did".

The validity of my statement isn't the issue, because I know what I experienced, and I wasn't going to back down out of fear. I opened the door and started yelling at him and telling him how much anger I have towards him. My mom then started saying "maybe you don't remember everything correctly. maybe he didn't mean to do what you said he did". Now, I don't want to tell what happened again for the 3rd time, as y'all see how it went last time, but just know I have no reason to falsely say this about my brother: he is jobless and has no money. I do not want comments invalidating my experience.

She then went on to say "why didn't you tell me this earlier. why did you wait so long" in a tone that expressed disbelief in my statement. I immediately went back to my room, packed up a few things, and left to stay with a friend for the night. These past few days, I have stayed at my aunt's place. The problem is, she has 3 kids and a full time job. There's no room or space for me, physically or mentally. I reached out to my older brother, 22M, and asked to move with him where he's at (across the country). He is getting a house in December, and has agreed that I can move in with him then. I have college classes here up until then anyways, so I'm stuck here for now.

The close friend that I originally confided in about the situation, 20F, lives 20 minutes from me, and has a spare room in her house. She lives with her parents and little brother. I really want to ask to rent out the room for the time being, but I am afraid of asking for too much or coming off as desperate. I don't want to live in a house with people who will disappoint me to the point of heartbreak. (There is other familial history that is too much to type, which I am in therapy for. This is the last straw). I do not want to roommate with strangers. What should I do?