Surgery usually involves releasing or enlarging the tight area of the tendon sheath where the tendon is binding. One treatment is simply to cut the sheath open and leave it that way. It heals back, but with more room - like letting out a pair of pants. This type of operation is usually done as an outpatient procedure under local anesthesia, after which a soft gauze bandage is worn for about a week. Cortisone shots usually provide relief, although this is temporary nearly half of the time.
Surgery provides permanent relief from locking and triggering in the great majority of patients.
Swelling, stiffness, aches and pains in the fingers may well be due to other problems, and may persist to some extent following any form of treatment. Many patients with trigger fingers also have a tendency to have swelling, stiffness and soreness of the moving parts of their hands, and that is not changed by surgery. With this in mind, the great majority of patients are improved with appropriate treatment. It depends on how much it is bothering you - it really is a quality of life issue. This is not a problem which can spread to other parts of your body.