Just an fyi for people commenting "Dur there is a BIG RED HEART, you can't miss it!" For people playing on PC there are also numbers that correspond to the dialog options, so it is entirely possible to pick your lines based on the paraphrase and not be aware of any of the emotion icons.
Also, some of the heart responses do come across as friendly or supportive rather than flirty, so it is understandable that someone would make the OP's mistake.
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You are in a rather unfortunate position OP, and it really depends on which heart icon you picked, which I'm not clear on.
The way the Dorian romance works is that certain hearts lead to certain other dialogs.
If you flirted with him previous to his personal quest (which you might not be aware of) and then afterward (back at Skyhold after the tavern) also picked the flirt when he says "Maker only knows what you must think of me now," you initiate the kiss in that scene.
If you previously flirted with him, but did NOT choose the heart when he says the above line, then do the scene with Giselle, on picking the heart option there Dorian is the one who initiates the kiss. This heart option is the one that says "this will start a romance with Dorian."
Fortunately for you, this particular path is buggy and the game does not properly register that the romance has started, so the "this will start a romance with Dorian" button is still there. You might be OK to finish the game with your Cassandra romance, but if it were up to me I would just scrap it and start over -- which is something that I have done, losing dozens of hours because I borked my play in some manner, so this is not an idle suggestion. Dorian doesn't like the idea of interfering if the Inquisitor is already romancing someone else, and will make a comment on that (depending on dialog options,) so you might see something along those lines if you proceed.
Regardless of which of the above paths you took, if you do decide to finish the game and you get a Dorian quest regarding an AMULET, DO NOT DO IT. This is the romance-only quest that triggers the relationship lock-in and/or sex scene. Sadly, you will just have to live with the quest and dialog option being forever open in your quest log, in addition to a guy you have to avoid talking to in Orlais.