The phrase make me can have a few different meanings in conversation. It could be used as a request for someone to do something, or it could be used as an expression of frustration.
If someone uses make me as a request, they are asking the person they are talking to do something for them. This could be anything from making them a cup of coffee to doing their laundry for them. The speaker is essentially asking the other person to make their life easier in some way.
If someone uses make me as an expression of frustration, they are likely feeling annoyed or exasperated with the situation they are in. They might use this phrase if they feel like they are being ignored or if they are not being given what they want. In this case, the speaker is not actually asking for anything to be done, but rather expressing their frustration aloud.