I agree with others here that appearance is regrettably important in general.
You ask about looking good for a romantic partner. I suggest you should additionally think about screening effects. Remember that, as a generalisation, the typical woman faces a different problem than the typical man when looking for a partner: the woman has to screen through a large number of offers, many/​most of which are low-quality, to find a partner she wants. People in general respond to screening problems with shortcuts and heuristics. A person who knows you well will consider your appearance as one aspect of what they know about you; a person who has just met you is likely to make a snap judgement on your appearance. Your aim should be for an appearance good enough that it is not making most potential partners screen you out at the first step.
I agree with others here that appearance is regrettably important in general.
You ask about looking good for a romantic partner. I suggest you should additionally think about screening effects. Remember that, as a generalisation, the typical woman faces a different problem than the typical man when looking for a partner: the woman has to screen through a large number of offers, many/​most of which are low-quality, to find a partner she wants. People in general respond to screening problems with shortcuts and heuristics. A person who knows you well will consider your appearance as one aspect of what they know about you; a person who has just met you is likely to make a snap judgement on your appearance. Your aim should be for an appearance good enough that it is not making most potential partners screen you out at the first step.