Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is well known that `Umrah can be performed during the time of Hajj or at any time of the year whether one has performed Hajj or not.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Your `Umrah is still valid even if you have not performed Hajj. The Prophet (peace and blessings be upon him), as well as the Companions (may Allah be pleased with them all), performed `Umrah before performing the obligatory Hajj.
Imam Ahmad, Abu Dawud and Ibn Majah reported on the authority of Ibn `Abbas that the Prophet (peace and blessings be upon him) performed four `Umrahs:
1- `Umrah of the Hudaybiyyah which he was prevented from completing;
2- `Umrah of Qada‘ (compensation) for the same in the 7th Hijri year.
3- `Umrah from Ji`ranah which was done in the 8th Hijri year.
4- Finally, the `Umrah he performed along with his farewell Hajj in the 10th Hijri year.
So, it is wrong for anyone to say that `Umrah is not valid if one does not perform Hajj.
At last, let me urge you to seek religious knowledge from those who are properly qualified to impart it. Those who dispense this kind of advice do not seem to belong to this group.
Allah Almighty knows best.