Is their size restrictions on bottles in your carry on?

3 Oz. No water or drink unless it's for your child

This is what TSA says: As a temporary exemption from the 3-1-1 rule, TSA is allowing one oversized liquid hand sanitizer container, up to 12 ounces per passenger, in carry-on bags. Since these containers exceed the standard allowance typically permitted through a checkpoint, they will need to be screened separately. This will add some time to your checkpoint screening experience. Please keep in mind that all other liquids, gels and aerosols brought to a checkpoint continue to be limited to 3.4 ounces or 100 milliliters carried in a one quart-size bag. For more information, go to https://www.tsa.gov/

They are allowing one 12oz bottle of sanitizer temporarily. 3.4oz is the general rule on other liquids

Yeah 3oz I usually put everything in a clear baggy so they can see it