@Veganbikechick, when I ride from my house to the Oregon Zoo, there are a couple of short, intense hills I have to ride in order to get onto the multi-user path that parallels along Hwy 26 and up the long, slow, steep hill to the zoo. I have always been able to do it from my very first time, but it was very difficult in parts. I know that if I do it periodically it will get easier, but there was this one hill that still "psyches" me up. I know I can do it but it will take 110% effort to get to the top and slowly. I just laugh now and do it - not let it get to me. I tell myself, "so what? I'll be out of breath at the top, but it will be a relief". I just do it. I shift to a low gear and just keep pedaling and looking at the ground just in front of me, not at the top of the hill.
Have you actually tried riding up that hill? How low of a gear were you in? I'd say that speed isn't a factor going up a hill unless you're coming down one hill and you want to use speed/momentum to help going up the next hill. If you're going up this hill from relatively flat, I'd just keep shifting into lower gears (before you need them) until you get one that is comfortable. When I ride up long, tortuous hills I'll tell myself, "I'll ride just to that mailbox", then once there I keep going and pick something else I'm going to ride to. I break it into smaller pieces and that makes me feel successful along the way versus making it to the top (or not) and using that as my success.
Hope this helps. Keep up the good work. Maybe you could "reward" yourself if you ride to work, say, twice a week?