Do I tell my daughter I think she may be on the spectrum?

Help! I have a daughter who I feel is probably PDA, possibly Aspergers. She has just returned from Brownie holiday, and literally exploded at me, because I asked her to wash her hands - this went on for four hours. For as long as I can remember, she has automatically replied with ‘no’, whenever I ask her to do anything. She is very negative, is very angry at home, quite aggressive, and has no respect for me as her mum, or her dad. She doesn’t seem to understand that we should be able to ask or tell her to do something - every request is met with a negative response. Tonight we have been going round in circles - she gets angry, we try and stay calm, give her some coping strategies etc., but she responds with a reason why she can’t do what we suggest. At school she is bullied, she doesn’t feel like she fits in, and doesn’t know why other kids are being nasty. She isn’t spiteful, and seems to save up her angst until she gets home, then just explodes at us. Her younger brother has complex special needs, and is diagnosed autistic on top of everything else he’s going through. My daughter knows all this - she also knows she is different, is scared that she’s autistic like her brother, wants help with dealing with her anger but doesn’t want to be the same as her brother. She is what I would call high functioning - incredibly able at school, but finding it increasingly difficult to keep or make friends. She thinks she’s different and doesn’t feel she fits in/doesn’t understand others. She wants to take the 11+ exam, and I know she will pass, unless she loses the plot on the day. I think she is PDA and possibly Aspergers. Do I tell her? We have spoken to school, but she is doing well, and they don’t see what she’s like at home. Not sure what to do - maybe some anger management counselling? Part of me doesn’t want to add to her anxiety by suggesting she might be ASD but then part of me thinks it might help. Not sure what to do next - any advice?