Having visited the USA numerous times over the years and being on the same combination as yourself, I can only say 'take your own'! Make sure it is in your carry-on bag (insulin and unpressurised, cold, holds do not make a happy combination) and you won't have any issues through Immigration etc. Plenty of ideas above concerning taking in tupperware (others are available!) boxes and we used a Frio pack when we went to Utah a few years ago to keep the Novopen cold whilst hiking. I think buying insulin in the US will be exceptionally expensive tbh and much cheaper and convenient to take your own.
All I would say is take slightly more than you think you'll need (you never can tell if you drop one and it cracks) and a spare pen for each type (same reason). Otherwise, have a great trip and just treat it like going to somewhere in the UK with a bit of extra travelling!