B737-800 flight attendant reported a fume event during departure taxi which dissipated once airborne and returned during approach to landing. The fumes reported were reported to the Captain who agreed with the flight attendant that an air quality check should be conducted by maintenance.

Narrative

We taxiied out and had to drive before takeoff due to the heavy snow. Then FA's (flight attendants) in the back called me to please come to the back to see if I could smell the fumes. I smelled it right away; started burning my chest; yes; nose.. started to feel nauseous as well as the 2 FA's in the back. We notified Captain immediately; he let us know that we were no where near any other aircraft and which way the winds were blowing and the fumes seemed to be coming from the deicer truck etc. He flushed the aircraft and that helped a lot. After take off we the crew checked on each other; Name1 was still feeling the effect of the fumes as well as me. Name2 was feeling a little dizzy but it went away. (Name3 could smell it as well while on the ground and passengers when she went to check as well towards mid cabin; it was really strong) So after takeoff; it was OK and we got a lot of fresh air. During decent after 10k I went to the back to check on the FA's and we could smell once again strong fumes. I mentioned it to our Captain and he wanted to make sure we were all OK and I let him know we have to report it. And he said that's good; they need to do an air quality check and left. We are now waiting for our ZZZ1 turn. No one met the plane and asked us about this. Do an air quality test on aircraft and notify Supervisors and who was suppose to meet us.