The claim that borax helps with inflammation and joint pain is false without a doubt.
According to the National Library of Medicine, although Borax is a low-toxicity mineral even naturally occurring in evaporate deposits, it is still harmful to humans depending on dosage with effects of reproductive and developmental toxicity, neurotoxicity, and nephrotoxicity. Based on these findings and more, Healthline agrees that Borax, while mostly safe to handle, should never be ingested for the sake of your health, with fatalities occurring in some cases, especially with small children. A study on the toxicity of Borax by Niels Hadrup, Marie Frederiksen, and Anoop K. Sharma, funded by the Danish Working Environment Research Fund, found that boron is indeed toxic, with toxicity after skin exposure including fatalities, as well as abdominal and local effects. They also found that "Oral toxicity endpoints in animals are weight loss and reproductive toxicity," but that their studies did not indicate a link between boron-containing compounds, like Borax, and genotoxicity/cancer.
Overall, it appears that most sources are in agreement between the toxicity of Borax and other boron-containing compounds, but cannot yet conclude that it is carcinogenic. I would never recommend ingesting Borax willingly and would also pay attention to food substances or other products containing Borax in the future.
Sources in order of reference:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2776007/#:~:text=Borax%20causes%20irritation%20of%20skin,unconsciousness%2C%20depression%20and%20renal%20failure.
https://www.healthline.com/health/is-borax-safe#safe-uses
https://www.sciencedirect.com/science/article/abs/pii/S0273230021000131