Hi, the word 'besides'...can start a new fact in a new sentence, but it is related to something in the last sentence.
e.g. The price of a cinema ticket is too high. Besides, I spent all my money yesterday.
'In addition to' ...needs 2 facts in the same sentence.
e.g. In addition to the high price of a ticket, the ice cream and drinks will cost me $6.
BESIDES can also mean "except", and IN ADDITION TO cannot. In spoken English, the words 'besides' has replaced the better word 'beside' in sentences such as:
Nobody has a key besides us.
I have no friends besides you.