I've been incarcerated before. Will this make it harder for me to get full custody of my child?
In a word, 'yes'. Previous incarceration can be a serious obstacle to custody, as most judges don't look favorably on a prior history that includes jail or prison time.
Your best bet may be to retain an attorney and seek some form of joint custody, establish a pattern of responsibly exercising your parenting time, and then consult with an attorney again to find out if seeking full custody is a realistic option.