Why do my bottom teeth feel like they're tickling when I breathe or talk?

Root sensitivity. My guess would be air moving through your mouth being noticed by exposed dentin on the roots of your teeth. You'll need a dental exam to confirm this but in the meantime, try a desensitizing toothpaste to see if it helps. If you have dental decay on your teeth, that could also be a culprit and you will need to get dental treatment to address that.
Abfraction. Did you have braces? Sometimes due to orthodontics you may have either recession or attrition on the enamel at the gum line. Both will lead to sensitive teeth. Sometimes it may tingle, but if place something very cold on it, it will hurt. Best to see your dentist. I am in las vegas as well.