Ask Mr. Smarty Plants

First of all, I'm not sure what your "red plum" is.   There is a native Prunus nigra (Canadian plum) that has as one of its common names, "red plum".  It isn't native to Texas, however.  It grows naturally in the Northeast, the Great Lakes area and into Canada.  Another plum called "red plum" or "cherry plum" is Prunus cerasifera, an Asian native.  Then, there are the edible orchard plum trees with two main types—the European (Prunus domestica) and Japanese (Prunus salicina) with several varieties of each.  Although some of these have reddish fruit, I haven't found one called "red plum".  The reason it matters what kind of plum you have is that some plum species are self-fertile and some are not.  However, even if they are self-fertile, they will produce more fruit with the correct pollinating partner rather than by self-fertilization.  There is an interesting article, Plums on the Prairies by Rick Sawatzky at the University of Saskatchewan in Canada that says that native plums of North America are good sources of pollen for hybrid plums.  The article gives information about whether various plums are self-fertile, but I couldn't find any information about whether native plums are self-fertile.  As fascinating as all this is, since I don't really know what your plum tree is, I can't predict whether it will set fruit if you do hand pollinate it. Besides there may be insects visiting your tree that you aren't seeing and they may be bringing pollen from another plum tree that is capable of fertilizing your tree.  However, I can't see how it would do any harm to give hand pollination a try.  Instead of a Q-tip, you might try a small paint brush. This is what Gregor Mendel used to pollinate his pea plants.  Best of luck!