Nectarine tree disease and treatment
You have several insect problems. The most serious problem is the black bumps which appear to be a terrapin scale. Each bump is a small insect which is protected under the scale and sucking sap out of the tree and weakening it. Scales are usually killed by applying a dormant oil spray in the early spring before growth begins. An oil spray now will burn off the leaves. The scale produce one generation of crawlers each year. Hopefully the crawlers should be coming out soon. Apply a fruit tree spray which contains malathion and/or a pyrethroid insecticide. The active ingredients are listed on the label be sure the fruit tree spray is labeled for peaches and look for scale and borers under pests controlled. Tree fruit tree spray mixes are available at many stores with a garden section or at garden stores.
If the trunk and branches of the tree was gumming you probably also have the greater or lesser peach tree borers.
If you get a spray for the borers be sure to spray the base of the trunk where the greater peach tree borer attacks. All the shoot growth from the base of the tree suggests you already have a borer problem. The borer sprays should be applied in early Jun and mid August.
The gumming on the fruit was probably caused by tarnished plant bug. If it was tarnished plant bug the damage is done and the pest has past.
Examine the fruit and see if there is a larvae in it. Also if you have gumming at the shoot tips If there is, It is the probably the Oriental fruit moth which attacks the young shoot tips in the spring and attacks the fruit later.
There are 3 or 4 generations of this pest each year. The damage was probably caused by the larvae of the first generation and you want to apply insecticide sprays to protect the fruit. The next generation will emerge in 2 or 3 weeks and you can apply a pesticide then. again you can use the Fruit Tree Spray mix which probably has Oriental fruit moth in the label as a pest controled. You need to spray at least twice for each generation. follow the first spray with a second spray 7 to 10 days later.