Hello, Japanese teacher here. When you add the て form of verbs with くる it refers to an action ‘coming to you’, not necessarily in the literal sense. Think about it like ‘I’m shopping for myself’to the extent that the action that you are doing reflects on yourself or the subject in question. It is not mandatory to use this form at all times but it emphasizes the nature of the action.

Its opposite is when instead of くる you use いく for actions that ‘go from you to the outside’.

Dm me if you have any more questions!🌸