Praise be to Allah.
If a fasting person becomes junub as a result of a wet dream or intercourse, he does not have to do anything, so long as that intercourse took place before the adhaan of Fajr. This is indicated by the fact that Fajr would come in Ramadaan when the Prophet (peace and blessings of Allah be upon him) was junub not as the result of a wet dream, and he would do ghusl and fast. Narrated by al-Bukhaari, 1926; Muslim, 1109, from the hadeeth of ‘Aa’ishah (may Allah be pleased with her).
Based on this, your fast on that day is still valid, but you should have hastened to do ghusl, because you have to pray, and the prayers must be done on time, it is not permissible to delay them.
Prayer is very important in Islam; it is more important that fasting or zakaah or Hajj or any other act of worship. Being lazy with regard to the prayer is a very serious matter, and some of the scholars were of the view that the one who misses a single prayer with no excuse and does not offer it before its time is over is a kaafir.
A warning is issued to the one who does not pray in the hadeeth in which the Prophet (peace and blessings of Allah be upon him) said: “Whoever does not pray ‘Asr, his good deeds are cancelled out.” Narrated by al-Bukhaari, 553.
For more information and commentary on this hadeeth, see question no. 49698.
The lady who asked this question has to repent to Allah for not praying and for being lazy about praying on time. Allah accepts the repentance of those who repent, and He forgives those who return to Him.
For more information see question no. 21806.
And Allah knows best.