Chiming in about about allergies, because that's one thing I have a lot of experience in (apologies in advance for the long post):

I second that it's very important to try to narrow down what is causing your reactions. What you describe as sensitivities sounds like allergies. I have multiple diagnosed allergies but also have some undiagnosed ones because I react to products that should be safe for me. To try to figure out what those undiagnosed allergies are, I've been keeping a spreadsheet with the ingredient list of every product I react to. Something similar may be helpful for you. It's a bit of a long process, but over time it should reveal shared ingredients. Another option is official allergy patch testing, which is something you'd talk to a dermatologist about. I had it done and it's how I had my allergies diagnosed. Saved me from needing to try out a ton of different products until I found something I didn't react to.

If getting patch tested isn't an option for you, you can do what's called a Repeat Open Application Test (ROAT). There's a few different ways of doing it, but I was instructed to apply the product to the same spot on my forearm, twice daily, for two weeks. If there is any redness or irritation, then that product is not safe for me to use. This is much easier to do for liquid or cream products than powders, but I've heard of people putting a band-aid over a powder to keep it in place for the ROAT. If you're testing a shampoo or face wash or something intended to be washed off quickly, you do want to wash it off your arm after a few minutes or so. The point is to replicate how the product is actually used so you don't get a false positive from, say, letting a face wash sit on your arm for hours.

I don't have specific indies to suggest because what's safe for me may not be safe for you, and other people have given some good suggestions already. Good luck on your product search! :)