What we were told and what I've personally seen with some kids is that the tests they use either don't measure sensitivities AND the test can be "normal" but with the substance they are sensitive too is VERY obvious by behavior every time it's taken away and reintroduced. It's often more accurate to go off the substance/food and see.
Some more tips from me
1. Praise praise praise! Catch her as often as you can being "good" or "quiet" or with a "calm body" and tell her how awesome she id doing being "quiet" or 'staying safe or calm".
2. Don't yell unless she is doing something or about to do something dangerous. You will feel like you need to yell at times, but that often will make things worse or more chaotic. She will not likely follow your direction if you are yelling.
3. Don't reprimand. Instead, when she does something "wrong" tell her to do exactly the opposite of what she is doing. For example: if she puts her hands near your 3 year old's glass and you think she is going to knock it over, instead of saying "Stop" or "Don't!", immediately like lightning get right in front of her, say in a calm 'indoor voice' while making eye contact, "Put your hands on your lap/down." Praise if/when she follows your direction.
4. Set up the environment to make it easier to prevent or react to her 'craziness'. If she is playing or engaged in an activity and you don't want her to mess with you 3 year old or your baby or the glass breakables on the other side of the room/house/etc., position yourself between her and whatever it is you want to keep her away from. OR make sure you have gates/doors closed, etc. Put things she continues to mess with or you are worried she might try to mess with out of reach or stored in closets/high spaces/tough to open containers. If she pours her milk out of a cup, next time, give her a sippy cup or literally hold the cup or move it out of her reach between sips/drinks.
5. If there are certain activities you anticipate being SUPER difficult or are just worried about something that could go wrong, find something special she can earn (trip to McDonald's or watch a special cartoon episode or something) if she does what she is supposed to do generally, for example without knocking stuff over, or without screaming, or whatever. But when you prep her for it, only talk about the positive to her. Tell her, OK, we get to go to McDonald's after ______ if you keep your hands and feet calm, your voice quiet, and your body and things safe.
Make sure (especially important) to praise her throughout when you see that she is following these 'rules' to remind her that what he is doing is going to get her something good in the end.
6. Sometimes, writing up (if she can read well) or making with pictures a schedule of the activities for the day can help reduce any frustration or high energy. Also, if you are going to do something that is not very structured or go to a place in which you can't structure everything (museum, zoo) explain to her beforehand what she needs to do or what her 'job' is (similar to above- keep safe hands, etc.). Include an incentive if necessary (trip to McDonald's or Cotton Candy at the end of the day - or once at lunch and once at dinner! or something that you think will be motivating for her) as well as a schedule that you can keep referring to. Getting a map in advance or online with different places/sites in the zoo/museum will help you create this schedule. After each activity/site visited and/or during, show her the visual schedule. Talk about "what we already did," "what we are doing now," and "what we will be doing next." Go through the remainder of the schedule if he wants to!
A lot of details I know, but if you try them, they will definitely help at least a little bit!