Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
You are allowed to perform extra Umrahs. If you are in Makkah, you should go outside the boundary of Haram: Masjid Aishah is the best option. It was the one that the Prophet, peace be upon him, told his wife Aishah to go to when she expressed her desire to perform Umrah as she could not do so as part of her hajj due to menses.
If, however, you are staying in Jeddah for a few days before going to Dammam, then you should assume ihram from Jeddah for in this case you the rule of the residents of Jeddah apply to you.
The scholars agree that the people of Jeddah who desire to make Umrah or hajj do not need to go elsewhere to assume ihram; they can do so from home before proceeding to perform Hajj or Umrah.
I pray to Allah to accept your Umrah and bless you with a safe journey back home.
Almighty Allah knows best.
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