Yes poor gut health can cause many health issues among which body pain. As according to Ayurveda, Vikrita Agni (abnormal digestive fire) can hamper the dhatu pusthi (overall nutritional deficiency). In your case it can be your Rasa dhatu & Asthi dhatu, Mansa dhatu got effected & not getting well nourishment.
Next Steps
There are two types of Arthritis so for exact diagnosis doctor consultation is needed and for both the Arthritis Ayurveda works like miracle
Health Tips
For vit D deficiency - exposure to sun is very essential (rising sun & the setting sun) , no other artificial supplements can work like sunlight.
For fatty
liver problem & Poor gut heath - sip on CCF tea 2-3 times/day & sip on luke warm water the whole day, cut off caffeine
Avoid late night & late rising
Getting up Early morning & exercises, yogas like suryanamaskar etc is essential