You're right to be concerned about your red oak tree. Oaks in the red oak and live oak groups (generally those with pointed lobes on leaves) are much more susceptible to oak wilt than species in the white oak group (those with rounded lobes on leaves, including white oak and bur oak). You won't be able to be certain that your red oak has oak wilt, you should have the diagnosis confirmed by a laboratory test. (Check with your state cooperative extension plant diagnostic laboratory or state department of forestry or agriculture about testing services.) However, you should suspect oak wilt if your tree has wilting, bronzing leaves that fall prematurely.
Oak wilt is caused by a fungus that spreads through water-conducting tissues, causing discoloration and plugging. Sap-feeding beetles, pruning tools, or root grafts may spread the fungus from tree to tree. Red oak branches may die quickly; within a few weeks of infection, the entire tree may die. Dieback in white oaks happens at a much slower pace. Prune out dead or damaged branches, taking care to avoid injury to healthy trees. Open wounds during the growing season attract sap beetles that spread the disease. Unless you are pruning out dead or storm-damaged branches, avoid pruning oaks except during the dormant season. If you have more than one red oak, consider severing the roots between the trees to prevent the fungus from moving from one to another. Keep trees growing vigorously by watering during periods of drought and by fertilizing periodically.