A friend who is seriously into astrology tells me that what you need to know is the exact year, month, day, hour, and minute (and preferably second, as well) of the person's birth. That is more important than knowing some "sign" attributes.
I am not sure, nor is she, about the "3 degrees Sagittarius" designation, other than it may be a spot in Sagittarius located 3 degrees from the ecliptic in the region of Sagittarius. If you can share more about that, it might help.
While there is no astronomical significance other than geometry, it may be astrologically significant that a given star "culminates" in Sagittarius at the appointed day and time. Depending on the date, this might even occur in daylight hours. And, if it's not astrologically significant, it might be significant enough for your purposes. A star "culminates" when it crosses the meridian at a given location, on a given date. The meridian is the arc that passes through celestial north and south and through the zenith at a given location. So, in order to determine a candidate star we'd need to know the date, time, and location of birth as nearly as possible. And then, of course, we'd have to hope there is an appropriately visible star somewhere in Sagittarius that is along the meridian at that time.
If we approach it given the numbers you cite, we could select something in the vicinity of -22.2 degrees declination, as Sagittarius is below the celestial equator. In addition, there are a couple of NGC (catalog) objects with "44" in their designations (NGC 6644, 6544, and 6445), but these are globular star clusters with many thousands of stars in each. Neither is near -22.2 degrees (both are between -24 and -25 degrees). In case you're not familiar with degrees of measure in the night sky, a degree is about twice the size of the Full Moon.
The right ascension hours in Sagittarius range from about 17 to 20, so you could choose an RA desgination and match that to -22.2 degrees. An RA of 17 hours, 44 minutes, and 4 seconds would be just within the western border of Sagittarius and there are a few naked-eye visible stars in that area.
It may interest you to know that this location is almost exactly 6 degrees north of the center of the Milky Way galaxy.
It may also be of interest that the Trifid Nebula (M20) is about 3 degrees east of the western border of Sagittarius, between -20 and -30 degrees declination.
But it's all guesswork until we know more specifics ... which is probably why many folks would rather shell out $50 and just go "buy a star". I think it's commendable you've chosen a different route!
Another way you can find an appropriate star is to use the online all-sky Star Atlas here to search that region for something you can use.
Almost all these stars will have a catalog listing, but very few have actual "names." Almost all star names are inherited from ancient catalogs and descriptions from the first true astronomers of what is now called the Middle East and Mediterranean regions.