Call the nearest children's hospital and make an appointment with a Developmental Pediatrican. This is not your regular pediatrician, this is a specialist who will do a complete evaluation that includes speech and langauge, OT, PT, neurology, ENT, educational, psychological and genetic evaluations if they are called for. You will miss nothing and have one report that gives you a plan to follow for her treatment. You may get a diagnosis, and you may not like it, but you will know exactly what you have in front of you and know what path to take.
In the mean time, contact the state early education evaluation team in TN and get them out to evaluate her, and take what ever you can get from them. If you are not satisfied with your speech therapist, find a new one and get as much therapy as you can. Call an OT who can see her sooner. If money is an issue, call Easter Seals, they can help with evaluations and treatment.
If she is going to be three soon, call your school district. They will be responsible for evaluating her and providing school based services (and she may quailfiy for more than just speech therapy) once she turns three. See if you can get the evaluation scheduled to coincide with her birthday instead of waiting for her birthday to start the process, it can take a while, so the sooner you start, the better. Ask for a copy of your rights from them, and read it. Find out how long they have to evaluate her, and meet with you, then make sure they follow that timeline.
Last, you obviously know that you have an issue and have done some research about what is and isn't OK. But be very careful. It is a mistake to say she can do any one thing and think that that may disqualify her from having the disorder you are thinking she may have. It does not work that way. Making eye contact is not what it seems. What she does with the information she gets from you when she looks at you is the issue, not whether or not she ever does. Likewise, pointing at pictures in a book so that you will tell her what it is, is not the pointing that they are talking about in the developmental screen. They are talking about pointing to gain joint attention for mutual language tasks. You are entertaining her by telling her what these things are and she is passive in the exchange.
It will be OK, keep working with her at home too, and get her as much therapy as you can, but get that evaluation by a Developmental Pediatrician. Time is one of the only things you will have that is free, don't waste it.