As someone who is ace as hell let me tell you that only you can decide what being ace means for you. Asexuality, like anything else to do with sexuality and gender, is a spectrum. Just because you're ace doesn't necessarily mean that you must be alone. You don't have to push people away for the sake of a prepackaged notion of an identity. If you truly feel something for someone, it doesn't make you less ace. Some ace people even engage in sexual activity with their partner, because they want to please their partner (or because it's pleasing to them to be doing it with their partner, etc.)
It's up to you to decide what you want.