A hand painted photographic portrait of a relative from 1910 sounds like a treasure! The sentimental value will probably be greater than monetary value. In those days, black and white photographs were often tinted by hand with water color, dyes, pastel, even oil paint. Some of these photos were partially painted while others were completely tinted.
The best monetary value will be in examples created by well known artists in that field, or in tinted photographs of famous people or significant subjects. To learn about the technique and the artists who excelled in hand painted photos, read "Early 20th Century Hand Painted Photography" by Michael Ivankovich.
You can find values by searching online auctions for similar items and checking the "sold" prices, not the offered prices. When you look around, you will notice that some examples are stunning while there are many examples of some rather ugly work, badly done.
Take care of your old picture. Keep away from sunshine and bright light. Avoid temperature extremes and humidity. If stored as just the photograph, wrap loosely in acid free tissue paper. For framing, find a professional who will use archival techniques and the proper materials to ensure the safety of the picture.
If you want to have the picture appraised, realize that the appraisal may cost more than the image is worth.