If you have additional problems with the friendship (the not talking for a different reason) then I don't see how you can make things "worse" through your honesty. Apologizing rarely hurts anything. While it's true your friend might be angry to learn it was you who did/started whatever, if they are already unhappy for another reason too, might as well "help" the situation by being honest and getting your own worries stable so at least you don't have to worry about being "found out".