Budgies are parrakeets (but not all parrakeets are budgies).
OP, you might like to read this thread, where I found myself in a very similar situation to you.
Basically…
-Don’t give up
-See if you can get the bird interested in a specific toy, then use this toy as a bribe to come near to/sit on you.
I’m of the opinion that mirrors make them antisocial (with everything except the mirror) - so if you have a mirror in the cage, I’d consider removing it.