Is it possible to perform Umrah from Jeddah for someone who intended Umrah after arriving there for work, or is there another solution?

What your friend said is incorrect, and your statement: "If I find time," means that you were not determined to perform 'Umrah before coming to Jeddah. If you decide to perform it while in Jeddah, then assume the state of Ihram from there whenever you wish. For Jeddah is a Miqat for its residents and for those who arrive there without intending to perform the rites but then decide to assume Ihram, based on the saying of the Prophet, peace and blessings be upon him: "And whoever is closer than that, then from where he started."