Yes, if I understand what 99Klein is saying here, I agree it's just conditioning.

Maybe the OP is gearing down too low on the hills in order to maintain the same feeling of effort they experience on the flats. Especially if most of the OP's riding is group riding, it would probably pay to go out on solo rides and attack some hills to build up both strength and effort threshold.

Also, a lot of cycling well is having the experience and confidence to know when and how much power to put down to get the job done. For example, as you approach a climb, it may make sense to power hard for a few seconds to carry your momentum up the hill a bit further, rather than dropping gears right at the foot in anticipation of the cadence you'll use on the middle and over the top of the hill.

Clearly, if the OP is hanging with the A group of a racing club after 5 months, they've got some power and fitness, so my assumption is that it's mostly a technique and conditioning issue.