Must things be arranged if I use Present Continuous for the future?

You can use the present progressive for future events, but they must have been arranged with another person.

A future arrangement is a plan that you have decided and organised with another person. [BBC]

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Instead of using the present continuous, I would use "going to" or "will." I outline the sentences below (and when to use each one).

If I decide today to wash my car tomorrow (but do not arrange it), I could write:

I am going to wash my car tomorrow.

OR

I will wash my car tomorrow.

In the first sentence, "going to" implies that you decided to wash your car before writing/saying the sentence; "will" in the second sentence implies that you came up with the idea to wash your car while writing/saying it.

For example:

I am thirsty, so I'll [I will] get a water bottle.

vs.

I am going to work out at 4 p.m.

In the first sentence, you are thirsty and immediately decide to get water, so "will" is appropriate. In the second, you have planned your workout, so "going to" is appropriate.