Say I like building things and I see an interesting product on the internet. Having seen this, and having the means to build something similar, the interest in the product, and the ability to understand how it works, is there anything wrong with borrowing public information about an object to use in building it myself? I would not attempt to share this object I built, for monetary purposes or otherwise. I would not claim ownership of the object. I would not assist others in building one themselves, aside from maybe showing them the publicly available information I started from as well. Is it legal to create this product and use it personally?
The title of your question suggests that a patent is involved, but it isn't clear from the rest of your question if that is really the case. Simply seeing a product on the internet does not mean that there are any patent rights attached to it.
If a patent does exist, then that patent's protection is defined by its claims. If you make or use an object that includes all the elements of the claims of a granted patent, then you are infringing that patent. It does not matter whether you share the object or attempt to make money from it—simply making or using it is enough to qualify as infringement.
That said, based on your intended use, the patent owner is highly unlikely to ever find out about your infringement. Further, even if they did, enforcing patent rights in court is incredibly expensive (typically involving multi-million dollar legal budgets), and they wouldn't stand to recover much from you, so it is even less likely that they would sue you for the infringement.