I've ridden almost 20,000 miles since August of 2003 when i started. A lot of cycling is mental. One of the first things that novice riders succomb to is wind and hills. Wind and hills can easily take the fire right out of you and want to make you turn your bike towards home.
Early on, i had to learn how to mentally process riding in wind and hills. The perceived lack of speed and adequate movement causes a newer rider to grow frustrated when tackling these obstacles. He/She feels like they are working very hard yet the bike is barely moving, so they grow mentally frustrated.
I learned to just relax and spin the pedals. Just look down at the ground and if it is moving, you are good to go. Just enjoy the ride. Now, I can ride into staunch winds and steep hills and often don't even think about it. It just takes time. Wind and hills slows every bike down. If you consider the fact that you are just like a grain of rice moving against a gigantic air mass, you soon realize why wind slows you down.
So maybe it isn't a different bike you need but rather, just practice with your mental abilities.