Overtime & Comp Time

Should I be considered a salaried employee or hourly?

When I was hired at my current place of employment I was hired as a salaried employee. I have a written agreement for a salary amount. When my paychecks come there is an hourly amount on it multiplied by 80 hours (for 2 weeks.) I also had a verbal agreement with my manager that any amount of "overtime" I worked would be used as comp time for when I need to travel, and if I went over the amount of "overtime" I had accrued, only then would I need to take time off unpaid.

Last week I took two days off for the Fourth of July weekend. I was told by my supervisor (not who I had an agreement with) that I needed to submit a time card. I informed her that I don't do a time card because I'm a salaried employee. She said that because I took time off, I'd need to take it unpaid. She said she discussed my "agreement" with my manager and was told that comp time was not an option.
I guess what my question would be is should I be considered salaried or hourly, and whichever I should be, should I be paid for overtime? As they are now saying that all those hours of "overtime" I worked (with the intention of using that time against my vacation) hours worked for free?

Another question I have is: I was told I should be in the office between the hours of 9AM and 5:30PM and I should take an hour lunch. Multiply this by 5 days in a week, and I come up with 37.5 hours for a work week. I figure that any hours worked over 37.5 would be considered "overtime" do you agree? I very rarely get time to take a lunch, therefore when I work 9AM-7PM I consider it a 10 hour day (7.5 regular + 2.5 O/T)

Let me know.
Thank you!
Overworked in Pittsburgh