Welcome to FlyerTalk, Tamcalinnyc.
From reports in
this thread, the hydrogen peroxide in Clear Care is a problem.
If less than 100ml, in a zip-loc bag, the bottle probably won't be tested & you can get through security with it. However, when carrying a larger bottle under the medical exemption, the liquid will be tested (open the cap, hold a test strip over it). The hydrogen peroxide may cause the test strip to react and you will not be allowed to carry the solution through.