Help! How can I heal my peach tree?

There are a lot of food safe pesticides at any local garden center for orchard use. You will definately need to spray the tree (usually several times a year). They also make very organic sprays if that is a concern for you with using manmade chemicals. It's not for me and the sprays work very well in warding off bugs. You did the right thing by mulching and pruning. Place a little fertilizer around the base, spray it with the pesticide, and if necessary place animal safe netting over the tree when the fruit is ripening to protect it from birds and I think the little tree will have good success. Also, depending on your variety of peach tree you may want to plant another peach tree nearby to encourage vigorous pollination. Peach trees are self pollinating however many times they will benefit from other peach tree's planted nearby. Good luck!