Current through a diode paralleled with a resistor
The problem is that I've calculated the current across the first resistor as 117.5 mA,


This is not correct. It applies only if the whole 4.7 V is applied across the first resistor. From your description it sounds like the 4.7 V is shared between several resistors and a diode, so you can't assume that the voltage across the first resistor is 4.7 V.