Declare and proclaim both mean to state something publicly. They can also mean to state something officially.
'Declare' is used when you state your earnings on your tax form.
"He declared his income to the government last year when he filed his taxes."
'Declare' is used in informal situations more.
"She declared to everyone at the office that she was going on a diet."
"He declared at the party that he and Penny were engaged."
'Proclaim' is used more for government declarations.
"The king proclaimed amnesty for all the rebels."
"The government has proclaimed an official holiday."
You could have switched 'declare' in the above two sentences. In fact, 'declare' is used much more often.