We don't use the signs when we look at interactions between people.
Now when you say your Sun is "square" her Sun, you are going by the degrees and NOT by the Sun, right?
If your Sun is at 2 degrees of Gemini, then ANY Sun between 24 Aquarius and 10 Pisces would be in square aspect to your Sun. And if someone had their Sun at 14 Pisces, it would NOT be square your Sun .. too far away from the square distance of 90 degrees.
Same thing with Moon opposite Moon.
IF your Sun is square her Sun, then there will be competition between the two of you, with of you trying to be in charge. Conflict and at least, irritation, as the two of you try to be the boss of the other.
This may not happen during the infatuation phase. .. it might take 2 or more years of being together to see it, but it will increasingly start to crop up as a source of conflict. Until, unless both of you learn to get a handle on your own emotional responses.
After all, astrology is only an influence on our inner dynamics, and the more self-aware we become the more we can choose our inner dynamics.
As for Moon opposite Moon, there is some disconnect between your emotional responses and her emotional responses. The two of you will never quite understand each other emotionally, even though there is a bit of attraction there. Understanding is the foundation for empathy, so it will be very difficult for both of you to adjust to each other, emotionally.
Unless one person has their Ascendant or Descendant conjunct (within 8 degrees of), the OTHER person's Sun OR Moon OR Venus OR Mars, the relationship is likely to die out within a couple of years at the longest .. maybe just a week or so. Or never even start up.
Unfortunately, in order to find someones Ascendant/Descendant accurately, the birthtime you use MUST be accurate within 4 minutes of the actual birthtime. So times that have been rounded off to the nearest hour, half-hour, or even quarter-hour just don't cut it.