Keep riding.
There is no "secret", exercise hurts....
Yup.
Sounds like your unfit. Only way around it is to ride harder and eventually you'll get fit enough to zoom up the hills in the biggest gear.
Couple tips: If it's your lungs/energy dieing then find a long big hill and make an effort to ride up it to the top. Repeat until you feel like your going to vomit. Do this at the end of your ride if possible so you still get in a fun ride! (If your into fitness stuff, check out HIIT)
If it's your legs that just can't turn the pedals then maybe get in some leg-specific weight training to help the riding. Build up the key muscles.
Otherwise just ride as much as you can (every second day max, you need to rest) and try and ride further and further each time. It doesn't actually take that long but give it 2-3months and you'll realize riding bikes when your fit is unbelievably fun! Keep at it, it will come.
I used to race bikes but I was off regular riding for like 1-2years. When it was time to get fit again (last year) I just rode further and further distances every week and found I was riding (over 30km) about 3km/h faster each week. It feels like shit starting out but now I purposefully point myself up hills because I find it fun!
EDIT: When you say your "Fit" what does that involve? It may be you haven't worked the muscles needed for cycling or your a little down on the cardio side of things. You could just be hitting the hills way to fast but I doubt it. Get into a nice cadence and stay a constant speed, Don't rush up the hills at full tilt, you'll just get half way and die.