Hi Zoelyn and welcome to the Breakfast Room. I also am self-taught and a late-comer to sax, although my previous experiences with many years playing guitar and childhood lessons on piano definitely helped. If you aren't going to learn to read music (I do, very slowly, but play sax totally by ear) you just have to keep playing to develop your ear or improvisational abilities. I often play on my own, just playing around with tunes, putting different harmonies to a well-known tune, or trying different rhythms, accents (using different tonguing etc) and phrasing. Sometimes I just improvise on a blues or something like that.
Sometimes I play along with whatever's on the radio or in my CD player, again trying to play the tune straight, or harmonising or embellishing the melody, or putting in 'call-and-response' licks behind a singer. I've also got a couple of the Jamey Aebersold play-along CD's which are good for practising jazzy playing.
The last thing I do is join in at jam sessions; usually the other players are sympathetic and helpful towards less able players, and you can pick up some good tips as well as getting the experience of playing with other musicians, which is great. I've been fortunate in that I have quite a good ear, and I pick things up quickly.
I don't really follow a rigid practise regime, sometimes I work on long notes, scales, arpeggios or different tonguing techniques, but mostly I just incorporate those techniques into my playing. I think you should approach your playing basically how you want to - you may feel the need later to learn how to read, or find a teacher, or you may be happy to continue playing by ear, it's whatever works for you really, and what you want to do with your playing. And how good your self-discipline is (mine's not very.)
I can certainly see the benefits of being taught, and am thinking of getting a teacher myself, more to make sure I haven't developed any really bad habits and to get technical tips rather than to formally study the sax.
Also, whatever method you use to play or learn, you're going to have those periods where you feel like you're stuck in a rut, but on the other hand you'll have bursts of quite amazing progress if you keep at it. Even after playing guitar for 35 years that is still true. The main thing is to accept the plateaus knowing that another leap ahead could happen at any time, and to enjoy it as much as you can.
Good luck, Bob