I'm assuming this is a business/first award, so in first class domestically on a 2-cabin plane?
You should be able to use the first class check-in in PHX and have the first class baggage allowance at check in.
As far as PHX-LAX, you can't be put in line for an upgrade. But if business/first award space opens on that flight, you can call & request to be moved to a first class seat (since you already "paid" the miles for it with the LAX-MIA segment).