My daughter has had phlegm for a week now, clear, sometimes white, no …

My daughter has had phlegm for a week now, clear, sometimes white, no temperature or cough, stool is normal, she's been drooling and having tantrums like how long have your kids had runny nose while teething? Should I go get blood drawn just in case it's an infection/bacteria all along? Her nose is sometimes stuffy, she's been dripping mucus constantly, thick, I wash her face all day so they don't dry up