If I am an alcoholic, does that mean I will also be more easily addicted to other things?

Definitly. Many people that have one addiction can be more vulnerable to other addictions either at the same time or down the road. All drugs of abuse cause a surge in Dopamine levels, this is what feeds an addiction so if one substance is removed another can come in, cause Dopamine to surge and drive the new behavior, be careful, have healthy support to boost dopamine, friends, family, exercise, meetings.
Probably. Addictions share a lot of similarities, even non-drug addictions such as eating disorders.