“Is it normal for your teeth to hurt after a dental cleaning?”

Yes

Teeth cleaning can sometimes cause soreness or pain depending on the depth of scaling that was performed.

Dr. Stoddart

No.  Once a week flossing is not enough. Flossing should ideally be done minimally every day before you brush before bed.  Proper flossing removes debris and with it some of the bacteria between your teeth where a tooth brush can not reach. It also breaks up the micro environment formed by the harmful bacteria harboring below the gum line.  It also introduces a little bit of oxygen which prevents damaging from living and growing.  We can not sterilize your mouth so even with the best professional hygiene treatment you still have damaging bacteria present.  Studies indicate that with 24 hours the harmful bacteria start to develop into damaging numbers and abilities again.  There fore you should be flossing a minimum of once every 24 hours   Floss before you brush so when brushing follows, the water and toothpaste can  rinse away the bad stuff and fluoride can get to the area to help prevent tooth decay by incorporating into the tooth structure.  At night because that is the longest time you go with out eating and at times the salivary  glands which help keep teeth healthy are not even working.

Yes. Especially the longer it has been since your last cleaning