I do not remember any trauma or any reason why I have severe shoulder joint pain only in my right arm, my shoulder aches even in a resting position! ?

Bursitis first choic. There can be many reasons for a painful shoulder and trauma is only one. It can occur spontaneously, be related to daily duties and activity, be due to bursitis, tendonitis, arthritis, torn structues, swelling, etc your evalaution will help clarify this.
That's not unusual. Not all causes of shoulder pain require a traumatic or acute event to become painful. Many causes of shoulder pain, such as adhesive capsulitis or rotator cuff tendinitis, begin gradually or just happen without an obvious inciting event. The bottom line is get your shoulder checked out by a doctor if it is bothering you.