Electrolysis depends on the skill of the therapist, so do consider going elsewhere and find an older lady with lots of experience. It's true that you can't always reach every hair follicle so it doesn't always work, but it is something that you need to persevere with for a couple of years!
In my salon we think the best treatment for facial hair is threading. Lots of asian ladies have facial hair all their lives and this is what they use. The hair is tweaked out at the roots and doesn't break, so the hair is slightly weakened and the regrowth is finer. You can also thread shorter hairs than you can wax. The problem with wax and sugaring is that it can be too hot for older fragile skin. Also you need to stretch the skin to keep it taut, which is much harder on aged clients.
You can learn to thread yourself, you just need to get ordinary cotton thread, tie the ends to make a long loop and then put both hands into the loop as if you were holding yarn for winding. Twirl one end of the loop through 360 degrees about 10 times so that you end up with several twists in the centre of the loop.
Now put your thumb and first finger into each end of the loop as if you were doing a sort of cats cradle and practice making first one end of the loop wider by opening your finger and thumb and then the other. You will notice that the twists in the middle move from side to side as you open the fingers first of one hand, then the other.
Practise on your legs and try and co-ordinate a sort of scissor action with your fingers and trap a hair on the moving side of the twisted cotton thread. The hair will get caught and will be whisked out at the roots. It's a bit fiddly at first, but you soon get the idea.
Now try on your face. You need to stretch the skin to be as unwrinkled as possible, so stick your tongue into your cheek to stretch the skin and use a good light and mirror. You don't need to be very good at threading to whisk off quite a bit of facial hair with a minimum of fuss. (Don't try shaping your eyebrows this way, there isn't enough control).
If you get into the habit of running a bit of thread over your face every couple of days, you will be able to cope with the discomfort and you'll never need to feel self conscious again.