What is the difference between 不由得 and 不得不?
不得不 = no choice but

不由得 = can't help (e.g. myself)

Example:


不得不屈服 no choice but yield
不由得怀疑我的眼睛 can't help doubting my eyes
(不由得 can be replaced with 不由自主地 in this example)



  At least 不由得 and 由不得 are the synonym


Actually they are two different things 

不由得 = can't help (e.g. myself); 由不得 = not up to (e.g. you)

Example:  

不由得怀疑 = can't help suspecting (不由得 synonym 不禁)

由不得你作主 = it is not up to you to decide (由不得 synonym 不到)

由不得我选择 = it is not up to me to choose (由不得 synonym 不到)