"I wanted this to be my wedding song, but was convinced otherwise." This is quite an unusual (and high-flown) use of "otherwise". It means what it seems to mean - that the person was convinced to change their mind. I think it's quite elegant, but I'm not sure I have ever used it myself.

Hi, "or otherwise" means that UNLESS something else is written or stated. Example: I have 10 photos, 1 of which belongs to another photographer. I put them on display. I write that they are all mine except for 1 - "unless otherwise" means - except if (used to introduce the case in which a statement being made is not true or valid). "unless you have a photographic memory, repetition is vital"