While you would be able to receive FMLA leave, you have to work for your employer for at least 12 months in order to receive FMLA leave, so you wouldn't be eligible.
You still may receive job protection, however, if you qualify as a person with a disability under the ADA or FMLA and need time off for that reason.
However, based on the conditions that you've mentioned, it may be difficult for you to be considered disabled, since your conditions don't appear to majorly impair your life functioning in a significant enough way.
I definitely think that it's a better strategy to inform HR about your concerns. However, it's also important to note that your employer is not doing anything illegal by making you clock in and out even though you're salaried. As a salaried employee, your employer cannot make your wages contingent upon the number of hours that you work. But your employer is free to require you to clock in and out even if you are a salaried employee.
This is due to the employment at-will doctrine, which is codified in California Labor Code Section 2922, and states:
"An employment, having no specified term, may be terminated at
the will of either party on notice to the other. Employment for a
specified term means an employment for a period greater than one
I sincerely XXXXX XXXXX had better news to give you, but I hope you appreciate direct and honest answers to your questions.