if designer indicates what current flows through node correctly you should ask if it is DC or AC current.. But unless it is really high currents it's don't care.
To set wire width use just rule of thumb 1mA per 1um for all the metal except top metal. Top metal can be thick so can carry more. See the design rules for your process.
For current you don't have to consider sheet resistance.
In case designer is afraid about voltage drop across the wire then you have to use the sheet resistance calculation. To get reistance of wire : R = Rsheet(ohm/square) * Length / width
and from there you calculate the drop.
If you have to use vias in the wire path like switching from M2 to M3 etc check how much current can via or contact handle(again check the rules) Usualy per via it's about 0.4mA/via and for contact about 0.7mA/cont as a rule of thumb