This is common for people starting a new exercise routine. If you had just done cardio in the past, then your body is not used to the type of workout your trainer did, especially if you were doing large muscle groups with little rest time.
There are different types of muscle fibers and cardio mostly focuses on the type 1 muscle. However, resistance training usually focuses mostly on the type 2 muscle fibers (a, b, x), however, these muscle fibers don't use energy as efficiently. During the non-aerobic breakdown of energy, circulating blood becomes acidic, it makes the individual light headed, and have nausea.
If it happens again, lie on your back and wait for your body to recover. Ease back into the workout. Eventually, your body will tolerate the increased acidity in your blood during workouts.
It happens a lot when individuals are not used to working large muscle groups: legs, chest, back.
Have your trainer increase your rest interval until you can tolerate shorter rest times.
(BTW, I have a PhD in muscle metabolism and am a CSCS and CISSN, so I'm not just writing some random old-wives tale. If you want the sources let me know, and I'll dig up the studies.)