You can have multiple assigned phone numbers on one account, and each conversation is tied to a particular phone number.

You can view this in the middle of the desktop app where the conversation says 'Via'

If the number that is tied to the conversation isn't available for texting, you'll see that the texting field is blocked out for that conversation.

You can create a new conversation with the same contact number using the correct number by updating your outbound caller ID, and then pressing the 'New Conversation' button in the top left, to start a new conversation.