Re: 2 1/2 year old doesn't talk + throws tantrums all day
I teach Pre school and also have a nephew with autism and many other disabilities. Also have worked in special education.
Definetly you will get some answers during an evaluation, but what they are is hard to say. Your child could be autistic, but there are other reasons a child may be a late talker and yes that can cause tantrums. A child by two has good cognitive ability and not being able to express themselves can be frustrating, leading to tantrums. The fact that he is making an effort to communicate such as taking your hand is a good sign.
He should be evaluated for hearing, hypotonia(low muscle tone, affects speech, eating and fine motor skills). Also, there are a number of language and communication disorders that can be helped with speech therapy.
NO matter what the outcome of the evaluation, there is a lot of great therapies, medications and other interverntions for children. I taught a toddler child once who cried all the time and had odd withdrawn behaviors, once he got his adnoids taken out he began to talk. Something about sleep apnea. I have also seen other children including my nephew improve drastically with early intervention. Be opened minded at the evaluation. They may throw a bunch of labels and terms at you but don't let that intimidate you. They need labels in order to provide treatment. MOst states have early intervention programs that are free.
IN the meantime, communicate with your chld in other ways. Make picture charts so he can point to things he needs. You can ******** picture icons on the computer for things like juice, milk, outside, video, etc. and glue them onto refrigerator magnets so he can point to things when he needs them. you may want to get a book about sign language for young kids, which teach basic, easy to learn signs such as more, want, yes, no, bathroom, etc. teaching sign language will not discourage your child from speech as many people think.
Also, your mother says it is her fault that she didn't talk to him and that could be true, but people also tend to blame themselves in these situations out of fear that there could be a problem with their child/grandchild. IF you do think that is the case though, don't hesitate to talk to your son all the time even if it seems he is not listening. Just because he doesn't respond back doesn't mean he doesn't understand.
Good luck for a positive outcome.