If lifting boxes "up to a certain weight" is not part of your job requirements stating on the job offer and it's out of your capacity to easily do it, you shouldn't do it, boy or girl, period. Gender is irrelevant to physical ability to perform a task. I'd rather not out to the boss to just avoid heavy lifting, she won't believe you, unless you are ready to fully transition on the job (in which case, you should start not with her, but with HR department) _and_ it doesn't guarantee she won't be continuing to ask you to lift boxes even if you fully transition.
I'd suggest to go to an HR and say that you were told to lift weights above your capacity by one of senior managers and you strained your back last time you did it and if it happens again, you'd hate it but won't have any other way but to go to hospital at company's expense. Hopefully, HR would be able to pass a message to the manager that it's not appropriate without you being personally targeted.