You already sent a message to ask if you can send a message. You already had their attention, why not just ask the actual question?
If the group can answer it, ask in the group. Unless you have nuclear launch codes to share, the group chat can handle it. There are probably 10 other people wondering the same thing who are too shy to ask.
If it's actually personal, just DM them with your question. You don't need to make an announcement first. Worst case, you get left on seen, and that answers "can I DM you?" as well.