I am curious what makes you think you have an S10x23.5 beam? In my experience, steel beams are rarely marked, you only know what size you have by carefully measuring all the relevant properties, then matching the beam up with a steel manual. Unless of course you purchased the beam from a steel yard, they would know what size you bought.
The currently manufactured steel beams that are close to what you say you have is a W10x22, or an S10x25.4. The numbering on steel beams works this way. The first number, 10 in this case, is the nominal depth in inches. The second number is the weight in pounds per foot of beam. The flange width, flange thickness, and web thickness are found on steel charts.
There are obsolete shapes going all the back to the early 1900's that have different sizes than current, similar shapes. You need to look at historical documents to determine the beam type you have, if it is more than about 40 years old.
One other detail is that the strength of the beam depends on the geometry of the beam, plus the strength of the steel. Modern steel beams are typical A36 steel, sometimes A60 steel, which tells you the yield strength of the steel. Older beams often used lower strength steel, so you really need to know exactly what you have before you begin to do calculations.
As to getting someone on an on line chat forum to determine if the particular beam you have is suitable for your specific application, that could be problematical. The folks on this forum who are capable of doing the calculations correctly may be professional engineers (like me), and are prohibited by law from doing engineering work without seeing the site, and having a contract. So the only folks on this forum who would consider offering an opinion are probably not legally qualified to offer a definitive opinion. So what exactly would you do with an internet opinion from someone you never met, who has never seen the site, and likely lacks the required qualifications to legally design your project?
Since you are in rural Arkansas, and may be unable to find a qualified professional, your best bet may be to go to a real lumberyard with your house framing plans, and let them size an LVL for you. A lot of the time a real lumberyard has an on call engineer who can size the beam, and stamp the plans (apparently not necessary in your case). The lumberyard simply rolls the cost of the design into the beam price.
You still need some help with the footing design and supports for the beam. Perhaps the lumberyard can help you out with those issues as well.
As for the installation process, be very careful to make sure you have adequate temporary support for the joists above during the install, improper temporary support can lead to collapse of the house. Best to have someone helping who has done this before, and understands exactly how to do the job safely.
