An experienced vet can check for arthritis by manipulating the joint: feeling for any restricted movement, pain indications, or un-smooth movement due to arthritic changes to the joint.
The fact that it took your dog three days to get over the vet examination implies that the vet was very through in the investigation and so I would imagine they would therefore be very certain of their diagnosis.
As the other poster said, X-rays do not always show the damage/changes depending on degree, angle, exposure of the x-ray etc.
It is also teh case that the degree of observable arthritic change does not correlate with the amount of pain perceived by the dog, a dog may be very painful with little observed change, or remarkably pain-free with a marked degree of change.
I had to take my dog off Metacam recently as it upset her stomach, vomiting and diahorrea, shame as it was great for her arthritic front leg
Non-treatment however can lead to more intense, more severe and less easily controlled pain in future as pain pathways can become hypersensitised and “potentated” due to long term, or even permanent, physiological changes along the pain pathways whereby shortcuts to transmit and amplify pain become established.
She is now on steriod tablets as required. Cortisone is an anti inflammatory so it helps settle down the pain associated with inflamation.
My previous GSD got to a point wherby she was on daily steriod tablets for two years when she was older for her arthritic back legs/hip dysplasia and that together with moderate regular exercise allowed her a good quality of life, including enjoying her walks, throughout that time
Weight and exercise are also important considerations with arthritis.
Any excess weight puts extra undue pressure and stress on the joints.
Exercise should be moderate and regular and tailored to each dog's individual circumstances
Too much exercise over stresses joints and increases/speeds up wear and tear /damage, particularly in the affected, roughened joints. It will also cause the dog to stiffen up afterwards as muscles react to unaccustomed exercise levels
Too little exercise reduces the dog's mobility, causes it to stiffen up and doesn't allow the degree of supplementary support provided by relatively toned muscles and ligaments.
Irregular exercise i.e. lots sometimes and little or none at other times, is the worse of both worlds; over stresses and aggravates joints without any chance to build/maintain supporting muscle and ligaments or to maintain mobility.
Glucosomine is usually given together with chondrotin and these are the building blocks for the production of cartilage, found on the ends of bones to help smooth movement within the joints. In arthritis this becomes damaged and eroded, leading to painful contact of eroded and irregularly reshaped bone ends. The idea is new cartilage helps to cushion this.
It is generally agree that glucosomine and chondrotin do not harm but there is less concrete evidence that they work.
Many people, who can report how they feel, take them. Some swear by their effectiveness, others feel no benefit.
Maybe they work for some and not for others, depending on individual circumstances