Hi.
Yours is a question that I get pretty frequently--help me Heather, I like my cousin! Half-cousin! Sister! Brother! Stepbrother! Stepsister! Based on this, I'd tend to think you can feel safe about being neither all that weird nor totally gross. It isn't that unusual for people to develop crushes on members of their family, whether nuclear, extended or step. When you're around people a lot and share many things in common, from mutual history to similar backgrounds to genetic codes, it can be easy to begin looking at them in more than a familial way.
That said, I'd have to say that getting romantically involved with anyone considered family, either by blood or marriage, is a terrifically BAD IDEA.
The most obvious objection to any such relationship is that the offspring of two very genetically similar people tend to have many birth defects. There's just not enough genetic variation to produce a healthy child and, therefore, a healthy human community. Such inbreeding is considered so bad that all states in the Union prohibit a person from marrying his or her sibling, half-sibling, parent, grandparent, great-grandparent, child, grandchild, great-grandchild, aunt, uncle, niece or nephew.
Even if you two never intend to marry or have children, there are many other issues you might want to consider. For one thing, mixing the business of romance with that of family can be extremely messy. Suppose you begin something with your half-brother and then one of you breaks it off? That could really complicate your life and the lives of the people around you. Another factor worth considering is the social stigma attached to such a relationship. People tend to react extremely badly to reports of incestuous relationships, even if they are consensual.
Finally, it's important to remember what you're feeling is just that: what you're feeling. You're not weird or gross and you shouldn't be ashamed of your attraction for your half-brother.
Of course, just because you probably shouldn't date your half-brother, it doesn't mean that your feelings are going to go away; it may be hard to totally forget them. And so you might ask yourself what you can learn from this whole experience. Especially at a time when you may have less experience with romantic feelings, thinking about what makes your half-brother such a great guy and why you are attracted to him may tell you something about other such feelings in the future--and about yourself.