Your child is not abnormal, she is just different.
But yes having a clear diagnosis would help, she definitively seems to be on the autistic spectrum.
Which doctors have you met? In my state, it was my pediatrician who directed us towards a state pediatrician specialized in detecting kids on the spectrum.
Diagnosis or no diagnosis, your child is young enough to be in the Early Intervention program (if you are in the US) - it's good for kids up to 3 years old. Speak with your pediatrician, she should be able to help you with directing you towards the right doctor and Early Intervention. Your daughter would probably benefit from sociabilisation classes, to help her go towards other children.
Well, if you suspect autism then the following signs and symptoms are indicative of autism: child is not really social and prefers to remain alone than in company; flapping of hands and other repeated body movements, going in circles, repeating words, repeating tasks etc; not maintain eye contact; no social smile; avoid words and prefers gestures etc.
I personally feel it is too early to worry. Your child is just 2 and half years old. Encourage her to speak, applaud her words, praise her, pretend you do not understand sign language, show flash cards and encourage her to verbally identify, play nursery rhymes and sing them with her, and may be let her be around her age children for a few hours everyday (say in a pre-nursery). If the child does not start speaking by the time she is around 3 years plus, consult his pediatrician regarding this. Take care!
The medical advice given should not be considered a substitute for medical care provided by a doctor who can examine you. The advice may not be completely correct for you as the doctor cannot examine you and does not know your complete medical history. Hence this reply to your post should only be considered as a guiding line and you must consult your doctor at the earliest for your medical problem.
it is never too early, the earlier the better. I have 2 daughters from my first marriage one has aspergers 11yrs the other childhood autism 5yrs. Both started out with little to no speech. My oldest now can speak very well and can carry a good conversation. My younger daughter is just now forming words and is able to follow some simple directions. But sill has a long way to go. I read in multiple places if they don't start to talk before age 6 chances are they never will. You need to see a child developmental pediatrician. The best are in CHOP care network
The ways to detect autism earlier are increasing. I definitely agree the earlier the better. Even if you don't have a diagnosis you can start getting her speech therapy. My daughter had been in therapy for a couple years before we were able to get her autism diagnosis.
talk to her doctor about your concern