Hi!
i am sure that it isnt a supply issue. if that was the case it would affect both your boobs.
It may well be that she is full of a cold and is uncomfy on that side. she might even be sore on one side - has she had any vaccinations recently?. and sometimes they just go off one for a while, mine did (and still does at 21 months!) at times. I can understand how frustrating it must be if you are getting sore on the 'good side'.
Like you said, trying a diff. position could help. Have you had any pain or soreness on the side she wont feed from? sometimes you can get blocked ducts near the nipple that can affect their ability to latch on.
The most important thing to remember is that one boob is more than capable of nourishing a baby, so dont panic if you cant get her back on to having both for a little while. Just relax and take your time, ok? If you stress about it then she will be stressed and its less likely to happen. Skin to skin contact is fantastic for encouraging them to feed: just strip her down to her nappy and yourself from the waist up, and just lay with her in bed and relax. dont try to feed her. just make it available and she may well just latch on all by herself
I am a trained peer supporter for La Leche League, so if you ever need any info or support i am only a PM away and would love to help. Good luck <3