Alto Saxophone issues!!!?

I joined my high school's jazz band this year, and since there are no clarinets in jazz band, I had to switch to Alto Sax. I have this problem: when I start on a G and go down, instead of the notes being low, they sound like they're up an octave. Please explain to me how to fix this in a simple manner; I'm not all that smart. ;-)
Thanks,
~Rachael

I forgot to mention that it is a regular G, without the thumb key (if that's what you call it, I'm used to clarinet)

The issue (as far as I can tell on here) is that you are using the clarinet embouchure when you should be using the saxophone embouchure, which puts the center of the sound very high. It is kind of hard to explain, but the clarinet embouchure is very high in the possible range, and the saxophone is nearly dead center. I created an image of it and uploaded it so you can at least get a better idea of what I am trying (and probably failing) to explain. The link is below.
When you play high on a saxophone, especially in the low range, it will automatically make the note jump the overtone series to the octave above it. It is just a matter of learning to adjust to the center instead of high in it.
Also, get a teacher. These are reasons why people have issues learning an instrument, and a teacher could tell you this quickly and probably demonstrate it better than it can be explained here. If you want to actually be good at the instrument(s) you play, get a teacher.

What you are actually doing is playing the 1st harmonic....

The reason could be one of 2 things.....

The most likely is that you are squeezing too tight on the reed when playing the low notes... Try loosening off and moving up the mouthpiece a little. Also a slightly harder reed might help.

This was the problem when I moved to saxophone from clarinet.... Unfortunately the mouthpiece was physically too large for me, so I bought a good metal mouthpiece which was smaller than the hard rubber supplied and similar to the clarinet mouthpiece dimensions and ...... It worked for me!

2. You may have a leak on one of your pads which will tend to make the saxophone play in the upper register.... If this is the case, you'll need to take it to a technician to fix it properly.

Hope that helps!

All saxophonists at one time or another have trouble playing anything below the staff. One trick you can try is taking your teeth off of the top of the mouthpiece for these low notes, and pushing up a little, emphasis on little, with your lower jaw if taking your teeth off alone doesn't work. You're essentially playing with a double embouchure when you do this, but it does work. And softer, not harder reeds make it easier to play in this range, but also create a worse sound in the middle and higher ranges, so if you can, stick with the reed strength you are using now. One other thing you can try, if you are starting directly on a low note and not slurring down to it, is key popping. Finger the low note except for one key, usually in the right hand, and then right when you articulate it, slap that last key down hard. It usually causes the note to pop out. But just don't use it in soft music, because the key popping really shouldn't be louder than the note you play.