OP, my younger daughter was delayed and was getting speech therapy at 18 months. I really think you need to have an evaluation done. It is definitely not too early to be concerned.
In my state, there is early intervention for age 0-3, and you can be referred to it by a doctor or you can also self-refer and just call them up. The evaluation is free, and if any services are deemed necessary, they may or may not be free. I would look into this ASAP before your child turns 3. Once they are 3, in my state, they are served by the public school system. There is a preschool aged system before they are kindergarten age. The requirements for entry into this program are different from the 0-3 program, and are certainly different in different states, but I think that a 3 year old who is not talking at all would likely qualify for speech services just about anywhere. Please look into these public programs.
Autism is not the only reason for kids to have a speech delay. As has been mentioned, there could be a hearing issue. But there could also be other speech issues. One of my daughter's friends has apraxia of speech (and for a while we thought my daughter had that too).
I would also recommend using sign language with your daughter. From what you describe, she is able to use her hands to indicate how old she is with her fingers. So it seems like she probably has the cognitive ability and manual dexterity to learn to sign. My oldest daughter (typically developing) knew hundreds of signs by the time she was 3, and my youngest (delayed) knew about 50 signs by then. We used the Signing Time video series, which I highly endorse. At one time it was on PBS, at another time it was on Netflix, I'm not sure exactly where it is now (certainly you can buy them at
Why use Baby Sign Language with your child?). If your daughter can't speak, she can still have language through ASL. Speech is a skill, and a way of communicating language, but it is not the only option for language development. Language is important for early learning, regardless of whether it is spoken language or not.
If for some reason sign language is not going to work, there are other technologies available to aid with communication. Our friend with apraxia used a book that had a lot of pictures in it of different things he might want to communicate and he would point to the pictures to indicate what he wanted. Later, this was converted into an app on an ipad that he would carry around as his "talker". He would touch the picture and the ipad would speak the word.
Some people are against using alternative communication (including ASL, PECS, talker apps, etc), because they think that it will be a crutch that the child will use and make it even less likely that the child will learn to talk, but that has not been what my research or personal experience show. My daughter (age 8) now speaks fluently and no longer needs speech therapy, and her friend with apraxia also speaks now, well enough that I can understand a lot of what he says (though not all).
As far as food, I know less about this, but when my daughter was in OT, there were kids there who would go to feeding therapy, so that is a thing too, which I think is probably related to a sensory sensitivity. I have been in parenting groups with people who had to tube feed their kids because of issues with this, so I would not agree with the poster who said a child will not starve themselves because of these issues. I would try to get an OT evaluation about this issue.
Note that if there is an underlying issue, it could take years to get a diagnosis (such as autism). But you can start getting services like speech therapy and OT based on the issues you see there even without such a diagnosis.