How to calculate Resistor needed in PNP Transistor Circuit
You should not use an emitter follower to drive that LED, the voltage drop is too high in relation to the supply voltage. 

If your GPIO is 5V you can still use the PNP 8550 transistor as so: 







simulate this circuit &ndash; Schematic created using CircuitLab

The value of R2 shown is probably a bit high, and depends on the LED Vf at 35mA. 

Incidentally, your measured voltage seems a bit high to me, you may be putting too much current through the LED for continuous operation. 

If your GPIO is 3.3V, you should use an NPN transistor such as a 8050 and flip everything around and reduce R1 to about 860 ohms. 

Note that LOW = ON in the PNP schematic shown, with an NPN transistor HIGH = ON.