Hi Sadie,
You are clearly being liked on dating sites because you have been able to talk to people who liked your dating profile first.
The problem that you are having with the lack of responses from profiles you like and message first could be in the type of messages you are sending.
Focus on sending messages that relate to something interesting in the person’s dating profile and ask them an open-ended question about it. This tends to get the best results in terms of generating responses.