Amy, if the company has an HR hotline like you say, it sounds like a big and established enough company to have a fairly robust non-discrimination policy. Can you look it up? It's often posted at the bottom of job ads ("XYZ Inc does not discriminate on the basis of race, age, sex, disability, gender etc."), and should be fairly prominently displayed on the HR webpage for the company or in printed HR materials.
Take a few days to calm down. Chat to your manager and explain that you're uncomfortable with how he's acting. If he's the good guy you think he is, he'll stop. Otherwise, your next call should be to HR. Even if they don't have a policy explicitly protecting trans workers, you can be fairly sure that they'd much rather not be known for employing sexual harassers like your boss.