i am looking into getting my duct work cleaned out as well, all of the register points have been swept out with the vacuum cleaner and they were bad, previous people i tell ya... but still the access i have is cleaned out. the system entirely is brand new.

Obviously you have a poor installer for new HP to be iced over after only one week.

Sounds to me like you got a typical gas n go recharge without tech finding out reason for the problem. And even at that, it appears the charge is still not correct.

Plan on more problems until you get a tech who knows what he is doing. Common reasons for icing over is leak and bad airflow. What supply temp are you getting? I assume from your post this problem was in AC mode.

IMO

Did you just get the outside unit replaced? I presume it was the indoor coil that froze over? Most commonly due to low charge or low airflow. Was the outdoor unit you replace also a 3.5 ton?

Get the guy back - tell him its still not working properly. have him measure the heat difference ("delta") between the return air and the supply air (should be ~20 degrees).