Hello,

Been playing probably longer than your parents have been alive.

Do long tones in front of a mirror and with a metronome. Start around 60BPM and do 4 beats, then down a half step four beats. then Refill lungs with a deep full set of lungs. Start middle C, go down chromatically to low Bflat, go back up chromatically. Go all the way up to high F, Then back down to middle C. Rest when needed. Eventually you will be able to do the entire range with out a rest as your chops strenthen. Concentrate on keeping your  neck relaxed and air stream open.

Long, boring and tedeous. But the results are what you are looking for.

Concentrate on proper hand position, hence the mirror.

Welcome and good luck

Hello and welcome! It's great you are learning on your own. There are some excellent resources on youtube.

Here is one of my favorite sax tone control exercises. 
https://www.youtube.com/watch?v=hqvB_uoOyGo&feature=youtu.be

Greg Fishman's Channel is great. He's a heavyweight player with plain spoken instruction.
https://www.youtube.com/channel/UCRWTWTQMCrWD-85qEES6whw

Army Field Band sax series is long but worth the study.
https://www.youtube.com/watch?v=EE8c_Z4g0-s

Jeff Antoniuk teaches sax and improv, etc. 
https://www.youtube.com/channel/UCC3oUqWa3fuURU3WbOWY3UA/

Best wishes for your musical journey!

-Rulon