'I am very tired from work' is fine, meaning you are worn out because you have been working hard. If you wanted to say you are fed up of your job, you use 'of' as the preposition rather than 'from'. I am tired of my work/I am tired of my job.

I would say "I had a very tiring day at work today",

I've googled it and no related usage. I think "exhausted" is more like what you described.

To be more clear, I would say "I am very tired from all the work I did." :)