Also I find having at least a warm up, better still a half hour warm up (could be scales, playing through a few tunes, could be letting rip) and then doing other things and coming back hours later and having a longer session (of whatever) is a very good plan.
It gives a better results with embouchure, technique, tone - the lot. If I can find time to space a couple of warmups during the day before a proper practice session or whatever I find it even better.
Loving playing scales is good!
Get to play all 12 major scales from whatever tutor or book of exercises you are using. Then memorise them until you can play them all from memory - pay extra attention to the ones you find tricky. Then play them one after the other in various ways - moving up by a semitone to the next scale, say, or going around the circle of fourths (or fifths, in the other direction). While you are doing this, get the best tone you can, and get your breathing sorted out.
A good exercise is to play a simple little tune (twinkle twinkle little star, anything) and then try to play it in all keys, working out the fingering in each key in your head and using your ears. You could start doing this with the eight keys you have now...
And do practice simple improvisation all the time... just little alterations to the melody, jigging the rhythm around a bit, 'ragging' the tune, 'jazzing it up' a bit.... it develops your rhythmic sense which it totally essential... and you can learn how to do clever improvisation on chord changes later.... and keep making it fun, you will make faster progress, which encourages you, which leads to more fun...
Lots of stuff to look at on Pete's 'Taming the Saxophone site!