"Miles ran" or "miles run" for axis label in graph

The correct form is "miles run".
To understand why, we need to remind ourselves that this is an intentionally shortened label, and that the purpose of the column is to show "how many miles you have run so far today". This is a sentence in present perfect tense (expressing an action that started in the past and has just finished). Present perfect is formed by the appropriate form of have plus the past participle of the acting verb. Because run is an irregular verb, its past participle happens to be identical to its simple present form. If you were measuring distance of other modes of movement, it could be "miles walked" or "miles driven" or "miles carried".

Miles run would be the correct label in this case.

You should use neither.

The title of the plot should contain information pertaining to the use of either words "ran" or "run".

The x and y labels should only be information pertaining to its coordinate label and unit (i.e. x (meters)). So for your case, the y-axis should be "y (miles)" or "y (miles/day)".