I don't know what these are inside your figs. However, my grandmother used to tell me that be afraid only of those bugs that eat (bite) you and not of the ones that you swallow, and think of these as just extra protein (if you can't remove them).

whirlmatt, here's a link to CSU's clover mite page, with tips for control. They list an organic control option -- "The best cultural control of clover mites is to try a little winter watering in those sites where the mites thrive - at the south and west sides of buildings. This can greatly retard populations increasing in spring." Doesn't help you right now, unfortunately, but you'll have a jump on next year. Here is a link that might be useful: Clover Mites

I am very sensitive to bug bites and have other allergies. If there is a mosquito in the yard it will find me and leave everyone else alone! I am a butterfly gardener and for years have brought in the caterpillars to raise since so many are killed by lizards, bees, and such. Up until this year, I have never had a reaction to the caterpillar spines of the Zebra Longwing. When I cleaned the cage where I kept the caterpillars and put in more plant food, I accidently rubbed my arm against the spines of a caterpillar that was under a leaf. A few minutes later, I noticed a raised oblong area that started itching. A little Benadryl gel helped over the next couple of days and the raised bumps went away. A couple weeks later, I got a few ant bites while gardening. Got out the Benadryl again but also noticed the same spot on my arm had raised up again and I didn't have any caterpillars inside to raise this time. I asked my dermotologist about it and she said that can happen, its the histimines reacting in your body. As often as I get bit, I'll be red itchy spots all over by summers end if every bit reoccurs. Maybe you are having a similiar response.

I agree with rhizo, or you could dump out all the soil and rinse off all the roots & leaves and re-plant it in a new pot with new soil. I have no idea what critters are in the soil, someone will come along with that info for you.