Allergy meds while breastfeeding?

So I’m only in my third trimester, but I plan on breastfeeding when my son is born. This is my first kid, so I have a ton of questions obviously. Anyway, I have awful seasonal allergies, I’m literally allergic to every single plant/tree that grows in my state. I’m also allergic to dogs and cats, but not severely, so I have two dogs and 3 cats. 😂 My dogs have been shedding really bad (they’re huskies) and I’ve wanted to take Zyrtec or Benadryl, but my friend told me it can dry up your milk! Obviously I don’t have any milk yet, but I know it can come in early sometimes and I don’t want to mess that up. I have my heart set on breastfeeding and I’ll be devastated if I ruin it. I googled to see if it was okay, and I didn’t see anything about allergy meds drying up your milk. So I guess I’m just confused. Is that like an old wives tale or something? Or does it only happen to certain people? I do know her supply is low as she is a breast cancer survivor, maybe that has something to do with it?