You are to be commended for figuring out all the scales on a saxophone "by ear". That is no small accomplishment!
If you can read the "alphabet" and can recognize the symbols for sharps and flats you can first learn how to "spell" the scales without having to learn to read the notes on the staff. The "Circle of 5ths" below can help. The musical alphabet goes from A to G.
You see at the top of the circle at 12 o'clock is the C scale which has no sharps or flats. It is "spelled":
C D E F G A B C When the scale gets to G it goes back to A and starts over.
Going clockwise around the circle is the G scale spelled G A B C D E F G, but in order to sound like a major scale it has one sharp which is F#. The order of sharps in key signatures is F# C# G# D# A# E# B# (same fingering as C). If you look to the left of C at 11 o'clock you can see the circle gives you this order. The G scale is:
G A B C D E F# G
The D scale is next with 2 sharps, then the A scale with 3 sharps and so on.
Write down the alphabet for 7 characters starting with D, A, E, B, then F# and C# for those scales at the bottom. Next add the number of sharps shown in the circle to the note names in the order shown in the circle going clockwise beginning with F. That gets you through the sharp keys.
The process is the same for the scales that have flats which go in the opposite direction around the circle. Start with the F scale: F G A B C D E F. You see by the circle it need one flat which is Bb. The order of flats are Bb, Eb, Ab, Db, Gb, Cb (same fingering as B), Fb (same fingering as E). The circle gives you this order going counter clockwise. I've done the first few to get started:
F G A Bb C D E F
Bb C D Eb F G A Bb
The 3 scales at the bottom of the scale are called "enharmonics" and can be confusing at first. We see 15 major scales on the circle of 5ths, but because 3 of them are "enharmonics" we say there are only 12 major scales. Don't worry if this isn't clear right now. As we become more experienced musicians it gradually starts to make sense---at least it did for me.
Cb Db Eb Fb Gb Ab Bb Cb sounds the same and is fingered the same as B C# D# E F# G# A# B
Gb Ab Bb Cb Db Eb F Gb sounds the same and is fingered the same as F# G# A# B C# D# E# F#
Db Eb F Gb Ab Bb C Db sounds the same and is fingered the same as C# D# E# F# G# A# B# C#