Hey, I was a firefighter myself before I had kids :)
One thing I know about fire department work is that it can be exhausting at times. Losing weight unintentionally can happen, but typically not that much even when you're doing extra work. Your symptoms suggest something is not right. I would go to see a doctor as soon as possible, have some blood testing done and see where everything is at. You need to be in top shape to be doing what you're doing - even in training. Don't delay in seeing a doctor, make the appointment today.
It sounds like it's time for a full physical exam. You mentioned that the doctor thought your heartrate was just a little faster than normal. But when was that? Have you had blood work done for thyroid? Losing weight, feeling full quickly, weakness, various aches and pains - that all adds up to needing a doc's help. Please get it checked out.
Perhaps a visit to the doctor would help.