No, because the primary intention of your first journey was to visit Jeddah and not Makkah. Although Jeddah is inside the mīqāt boundary where ihram must be worn, your destination was not Makkah initially. It may be that you must remain in Jeddah for a longer period than you anticipated. Once you intend to leave Jeddah for Makkah, you will be like a resident of Jeddah and will assume iḥrām from where the people of Jeddah normally do.
Shaykh Mustafa Umar