"у меня получилось" is "I completed something / I got something right". It may be cosidered as shortcut of "У меня получилось это" = "I have get it".
"Меня получилось" has no sense. "У" is mandatory. "получиться" is something like "to happen in the right way". But "in the right way" can be cancelled by explicit statement. So "у меня получилось = I got/did something right" vs "у меня получилось дерьмо = I did something bad / I got some shit". So whole phrase can be decomposed "Something of mine (у меня) happens in the right way (получилось)".

Мне пришлось = I had to
yes