Usually "what should we/I do?"-Questions are off-topic as they are advice requests and can hardly be answered without being opinion based. I strongly recommend you to rephrase your post!
Therefore based on your post, I will answer the question as follows:
- How can we verify whether it was menstruation or virgin blood?
Virgin blood is usually of lighter red colour -as it is fresh blood- and it usually is only one or two drops. While the menstruation blood has a darker colour. (My source and here a second one in Arabic)
- So what if we had intercourse during her menses?
That would be a big sin as Allah said:
And they ask you about menstruation. Say, "It is harm, so keep away from wives during menstruation. And do not approach them until they are pure. And when they have purified themselves, then come to them from where Allah has ordained for you. Indeed, Allah loves those who are constantly repentant and loves those who purify themselves." (2:222)
The scholars hold different opinions on whether or not a kafarah is necessary, according to imam al-Qurtobi (see here under -الثامنة ...-): Abu Hanifa, Malik and a-Shafi'i hold the opinion that the only thing he has to do is repentance and asking Allah for forgiveness. While imam Ahmad considered a kafarah necessary based on a hadith:
The Prophet (ﷺ) said about a man who has sexual intercourse with a menstruating woman: He should give one or half dinar as sadaqah. (Sunan abi Dawod and other hadith compilations)
This is also the prfered choice of at-Tabari who said if he didn't it would be fine too. A Shafi'i held this position while he was in Baghdad too. Others said that if intercourse happened during menses one dinar is the kafarah if it was at the end half a dinar.
One dinar is 4.25 grams of gold according this fatwa
According this the minimum you should do is repent and avoid having intercourse during the menses in future.