Would there be any efficacy in taking 10 mg of Prozac (fluoxetine) for anxiety/depression I am extremely sensitive to all medications/antidepressants?

Low dose Prozac (fluoxetine) . If still symptomatic and if normally medication sensitive it's reasonable to start at a low dose with the goal of titrating slowly to a standard therapeutic treating dose to get optimal results. Some even use alternating dose days. For example 10-20-10-20. If unable to tolerate would consider alternative medication or an adjunct to the Prozac (fluoxetine) .
Possibly. Usual starting dose is 20 mg but it is not unreasonable to try a 10 mg dose. Usually want to give it 3 to 5, even potentially six weeks if you're tolerating it okay.