I've changed both sides without taking the headlight or wheelwell spash shield off, and yes, it's extremely tight.
The trick is you have to hold the wires to rotate the bulb.
Anyway, did it look like it was burnt?
You know, my car is 1.5 years old with 14,000miles/23,000km and both sides burnt out, that's kinda strange.
My other car's signal bulb lasted 5-6 years at least.
I took it to the dealership and they said it's suppose to look like this.