Why dentists say you shouldn't rinse after brushing

That's the acid from the apple wearing your enamel down. The "squeak" is from the increased friction on the surface of the teeth.

You can get the same feeling from a Coke.

Or you can try gum/candy containing xylitol.

excerpts from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4232036/:

    The recommended dose for dental caries prevention is 6–10 g/d....

    Xylitol reduces the levels of mutans streptococci (MS) in plaque and saliva by disrupting their energy production processes, leading to futile energy cycle and cell death. It reduces the adhesion of these microorganisms to the teeth surface and also reduces their acid production potential.

    ...Thus, xylitol inhibits S. mutans growth essentially by starving the bacteria. Xylitol can inhibit the growth of harmful oral bacteria such as S. mutans, but its benefits do not stop in the oral cavity. Xylitol alcohol has been shown to impact growth of nasopharyngeal bacteria such as S. pneumonia and S. mitis, and hence has a role to play in nasopharyngeal pneumonia.

    Xylitol decreases the incidence of dental caries by increasing salivary flow and pH and reducing the number of cariogenic (MS) and periodontopathic (Helicobacter pylori) bacteria, plaque levels, xerostomia, gingival inflammation, and erosion of teeth.

    The predominant modality for xylitol delivery has been chewing gum. Chewing gum accelerates the processes of rinsing away acid and uptake of beneficial calcium phosphate molecules to remineralize tooth enamel. The recommended length of time for chewing after eating is approximately 20 minutes.

    Consumption of xylitol chewing gum for ≥3 weeks leads to both long-term and short-term reduction in salivary and plaque S. mutans levels. A decrease in caries incidence has been reported among children exposed to the daily use of xylitol for 12–40 months. The long-term benefits have been observed up to 5 years after cessation of xylitol use. A prospective controlled, double-blind clinical trial confirmed that MS levels in plaque decreased as exposure to xylitol increased. However, a plateau effect was observed between 6.88 g/d and 10.32 g/d. The caries preventive effect was observed to be long term in relation to the teeth erupting during the period of xylitol use.