Will this bursitis pain last forever?  

No. Bursitis of the trochanteric bursa (side of the hip), and subacromial bursitis (shoulder) are among the mowst common rheumatology problems seen. They can arise from arthritis, or simply exist by themselves. A cortisone injection, if bursitis exists, almost always gives quick and good relief! if it doesn't, chances are you do not have simple bursitis!
No. Bursitis pain, although not lasting forever, may definitely feel like one doing so if left untreated. If it doesn't go away after stopping the aggravating movements/activities, taking simple anti-inflammatories such as Ibuprofen or naproxen, ice/heat applications, it may be time to see your doc for a more aggressive treatment approach.