I'm not clear why your path in life being determined precludes you from taking responsibility for your actions.
Presumably if the universe is deterministic, then the consequences of your actions literally follow from your choices. Therefore the proximal cause of those consequences can be attributed to you, ie. you are responsible for causing those outcomes.
That you were determined to make those choices doesn't erase this basic fact. That you can learn from mistakes and make different choices in the future given similar circumstances is exactly why holding you responsible for your choices works as a form of moral feedback.
If your choices were not deterministic, then this implies that they were partly random, in which case holding you responsible is no longer a valuable tool for moral feedback, because no amount of responsibility or feedback can influence a random variable. Therefore, the degree to which you should be held responsible is arguably proportional to the degree in which your choices are deterministic; we see this in every day life, where babies and the clinically insane who act for no apparent reason are not held responsible for the actions, while people who are mentally competent and can operate within systems of rules are held responsible.
Which means there is no consistent self which can determine them.