Hi
There are various ways of Progressing planets but the most common is one day for one year, called Secondary Progressions. The Sun travels through signs at approximately one degree per day. Assuming you were born with the Sun at or about 2 degrees Scorpio, your second year would be progressed Sun at 3 degrees Scorpio, third year, Sun at degrees, etc. Around your 28th year your progressed Sun will move into Sagittarius, as you have been told.
Firstly, should you stop reading Scorpio horoscopes? I don't put much faith in such columns but the answer is basically No. What is likely to happen is that you Scorpio Sun will be 'tinged' with a Sagittarius colouring. Around 58 your progressed Sun will move into Capricorn and then you'll have a 'Capricorn tinge'.
Secondly, the other planets (and indeed Ascendant and other angles) also progress. The two most common ways of progressing are secondary progressions, again based on a day for a year. However the movements of the planets vary, so in a day your progressed Moon may travel around 12-14 degrees whereas progressed Saturn may move only a small fraction of a degree. So if you look at your secondary progressed chart for age 28 the Sun may have just moved into Sagittarius but the other planets may be in widely diffrent relationship to your progressed Sun than they were to your natal Sun.
Some Astrologers use Solar Arcs, and will progress ALL planets by the Sun's mean daily travel. So the basic relationship between the planets remains the same. You will find other variations of progressions as well.
If you are going to deal with them the best way is to get someone to cast your progressed chart for age 28 (or the date at which your progressed Sun enters Sagittarius) and then get this interpreted relative to your natal chart. Newspaper horoscopes just can't cope with this sort of analysis.
