Is nominal/real income and nominal/real wage the same? If so, is it possible for your nominal income to rise as your real income falls?
Wages are a subset of income.  Your income includes your wages but it also includes other sources of income such as dividends and interest.  If your only source of income is a job, then income and wages are the same thing.

It is certainly possible that nominal wages would rise while real wages fall.  Imagine that you earn 50,000 at a job in 2019.  Inflation runs at 5% a year.  And say that at the end of 2019 your boss says that you're getting a 2,000 raise so your salary in 2020 will be 52,000.  In nominal terms, your wages increased from 50,000 to 52,000, a 4% increase.  But since inflation was 5%, your 52,000 salary in 2020 will buy less than your 50,000 salary bought in 2019-- you would have needed a 5% raise (2,500) in order to keep pace with inflation.  Your nominal wage increased but your real wage decreased.