If I have a sensitivity to chicken fat, should I try and get chicken with low-fat content (skinless chicken breast)? Or am I okay to eat chicken skinless thighs that have a higher fat percentage?

It may well be that the fat content is too high which may be taxing the system currently. The reason for this could well be that under your results "Digestive Process" the digestive enzyme appears to be orange. Lipase is an enzyme that the body uses to digest fats and where it is orange it may mean that it is slightly depleted due to the heavier consumption of fats.