I should add one bit of advice for the OP.

There's no harm and plenty of good in stopping for a minute or two when you run out of juice on a climb. You'll be amazed at how much you can recover in a short break. Ideally you want to top the hill on the next surge. Try to get at least halfway, or better yet two thirds of the way up before stopping, because what you can cover between stops will get progressively shorter.

BTW - I refer to a certain class of hill as "bite size". These are hills that you can attack on a single hard effort, drawing on your reserves and topping before they run dry. We all have our own bite size hills, but just as with candy bars, "bite size" varies with the individual. But the concept is a useful tool for climbing.

Go out and find some hills. Attack them as if there were a big dog behind you, go as far you can before crapping out. Make a note of how far you got this way, subtract about 10% and that's bite size for you. Hereafter, it's a question of gauging hills and deciding whether they're bite sized or need to be broken off and chewed over time. Using the bite size concept, and attacking select hills will save time on your rides, and in the process make you a stronger climber.