Speaking from personal experience, I can tell you that spring in West Texas can be rough on my allergies. Lord knows we have plenty of potential causes in our region - blowing dirt, dry conditions, blooming plants - but one cause that many of us have never considered are the fruitless mulberry trees in Many older neighborhoods on the South Plains and Permian Basin.
Neighborhoods in older areas of towns in our region had these trees planted during the housing booms post World War 2. These trees are big, beautiful, and are nearly impossible to kill on accident. All of these factors make for a resilient shade tree in a generally inhospitable area.
I'm no physician, but I can share with reasonable certainty that the allergy problem manifests itself in the spring - as early as February, but seems to peak in March and April. Each year allergy sufferers struggle through these months - especially if they live in older areas of our cities and towns. The cause could be fruitless mulberry trees - as I've learned these trees are tremendous pollen creators! In fact, several major metro areas in the southwestern US banned the planting of these trees decades back.
3 decades into El Paso’s ban on new mulberries, existing trees are nearing end of life
In addition to the problems associated with allergens caused by these trees, I can also tell you that older plumbing lines are highly susceptible to their root systems. You see, because these trees are so durable, they are therefore experts at locating moisture in our dry climates. Believe it or not, mulberry trees are heavy users of water! Sometimes, for the tree, locating that moisture is easy; and so another leaking plumbing drain line soon becomes an entry point for tree roots. It's not unusual for sewer line replacements completed in older neighborhoods to be due, in part, to this particular tree.
Also, many foundation problems are caused by intrusive tree root systems. Trees and vegetation (regardless of type) planted too close to a structure are a common cause of foundation issues because the tree is, again, searching for moisture. However, even trees planted a reasonable distance from a structure can still cause problems for the foundation if the tree is always struggling to get something to drink!
So how can you avoid the challenges listed above? The simplest choice might be to remove the tree! However, I don't blame you if you don't want to - I've got 2 fruitless mulberry trees in my yard! They provide outstanding shade in the heat, and are very durable trees! I'm certain I'm saving money during the summer because these trees keep a large part of my home shaded daily during hot temps!
Your next best solution might be to keep them watered near the tree trunk, so they're not searching for moisture under your home or near a sewer line. If they can find water near the trunk, those pesky root systems might not work so hard to damage your home or plumbing system.
Additionally, you might consider improving your homes insulation levels in the attic, and sealing off potential air leaks wherever they may be found to assist with allergy reduction. Older homes are not generally very energy efficient, so sealing gaps and cracks at windows, doors, floors, ceilings, in the attic, etc, all could help a little with this situation.
These are not fool-proof solutions (eventually you'll have to go outside!), but they could improve your quality of life, and reduce potential repair costs on your home in the future.