Ask your bike shop what it would take to put lower gears on your bike. The simplest and least expensive swap would be a new cassette (rear cog set). How low you can go with that, depends on your rear derailleur.

Training for hills is like training for anything - take them in small chunks at first and build. Do hill repeats. If there's a hill you can get all the way up, do it over and over again - if not, then just climb for two or three minutes, turn around and go back to the bottom, then do it again, and keep doing it until you're worn out. Do this once a week, and also make sure you schedule rest days into your training plan - rest days are when you actually get stronger from the stimulus of your workouts!

Make sure your nutrition is good, both off and on the bike. Women especially often need to eat something during a workout longer than an hour or two. Running out of calories (stored glycogen) during a workout doesn't usually feel like hungry, it feels like tired and weak. You might need extra protein while you're building muscle, depending on what your diet is like - especially after a hard workout.

Don't be ashamed to get off and walk when you need to. Most everyone does. Better to do that than to wait until too late to unclip, as you found out. (Hope you and your bike aren't too banged up!)

Being small and light is actually a big advantage on hills. Before you know it you'll be leaving the big guys in your dust.

And - welcome to TE!