This means I can't do it as often as necessary. Is there a way I can do this alone ?
The way I always did it was to cuddle them in very close across my body - almost in a breastfeeding position - so that one arm has not only control of the arms, and head, but can also hold the legs.
If they are too big or strong, you can try swaddling first - then it is very easy. You just need to keep the head tucked in close, and put up with the disapproval :-)
Have your tried asking her to blow her nose with a tissue recently? My 21 month old can blow his nose if I hold the tissue in the right place for him. I discovered this when he got his first cold for a while when the weather started to get cooler. When he had colds before the summer when he was a bit younger, he couldn't blow his nose but when I explained it to him this time, he understood and managed to do it. We also demonstrated and he got the idea quite quickly.
I realise we are quite lucky with this and not all children can blow their own nose at this age. But I would think it's time to start encouraging her to give it a try. I can't imagine many 2 year olds still being that happy with a nasal aspirator. One thing that could help with the learning process is to do it after bath time when the mucus should be looser due to being in the steamy environment. You could also get her to practise blowing with her mouth to understand what it means to breath out hard, then transfer the technique to blowing through her nose.