Did I do right or wrong when I did not tell my friends that I was going to the mosque to pray, for fear of showing off, after I had announced to them the time of prayer?

Your notification to the person mentioned, regarding the entry of the prayer time, is sufficient, and you are not required to inform him of your going to the mosque. However, informing someone of your going to the mosque is not considered showing off (riya') if the intention is to encourage imitation. You should also have notified all your friends and urged them to pray, as advising the negligent is an obligation.