Extremely Stiff Action

I've been playing saxophone for a number of years and have pretty much only had experience with one horn (my own) as I grew up in Brazil and was satisfied with it because it was all I knew.

Unfortunately as i am now in music college I am having a hard time playing repertoire that require more speed. (Up till now i always played by ear and if I couldn't do it one way i would just to another way...) Now in college some of the pieces I play require a great amount of speed and I just can't play them because the action is so heavy. My instructor was really surprised by the amount he had to press down to get a sound out. The problem occurs especially in high D-F# and low C-Bb.

Is there any cheap way of getting this fixed? What is the amount I would be looking at paying? I imagine that if you change the action you would have to change the pads as well...

P.s. I'm playing an old Conn 20M...my Instructor wants me to just get a new horn but financially it just isn't feasible...Thanks so much for any responses!