Yeah, you're in a bit of a jam. If you can't get help from America or any other civ, your best bet is probably as follows:
1. try to defend that size 11 city you've got there. If the Aztecs attack it, you've lost the city. Try to starve down the populace some first, conscription if you have nationalism. But, if they don't attack, it shows they're going for a "war of attrition" and you've got your work cut out for you.
2. If the Aztecs attack and capture it...
Abandon the cities immediately south, pillaging as many railroads and roads as possible. You need to slow the advance as much as possible to give your units a fighting chance. Rush defensive units and artillery, for preferably defensive countermeasures. The artillery will wear down the stack, and with no city to heal in, they will be forced to either fortify where they are, (which leaves them vulnerable), or retreat.
3. If the Aztecs work on pillaging...
No need to pillage or abandon your own cities, they can't use the railroads against you. Start rushing defensive units and artillery (offensive units if you have one that has an attack of 5, 4 is pushing it). Use the artillery, wear down their stack. Defensive units need to be posted on important avenues of transportation, or resources. Use offensive units to finish off retreating enemy riflemen (they won't fortify in your territory).
Also, move non-essential defensive units from your core cities to the front line, perhaps even leaving a few undefended. Your railroads will allow a fast response if anyone lands on your shores.
That's about it. If the Aztecs concentrate their firepower and use their fast units (knights) effectively, you're screwed. But, the AI has continuously shown this to be not true, they are always very inefficient. I've faced far worse invasion than this, and survived. Some of the most epic battles ever fought occurred under my command.
Good luck, soldier!