"is it also right if they didn't acknowledge your sincerity?"

For me, it is only the person who knows the depth or sincerity s/he afforded to others that can know, therefore whether they accept/acknowledge it or not is the least of your problem. The way to show how sincere you truly are is to forget there was a problem in the first place after the apologies have been rendered. And if they treat you back right, then all is forgiven.. :)