Go in to work has a very specific meaning that implies physically travelling to one's place of business. Go to work can be used to imply focusing one's attention on a task. This usage could also be expressed as "get to work", which refers to focusing on a task or responsibility.

The first *generally* implies your place of work is away from where you are, and towards the centre of some place - a town, a suburb, etc. For instance, if I lived in the suburbs and my place of work was downtown or generally in the direction of downtown then I could naturally say "I'm going into/in to work". It would be less natural to say this if it were the opposite and my work was in the suburbs and I lived downtown. The 2nd is a more general expression that can work in any situation. It would work for the above situation where we used 'in to', but it would work in all other situations too.

1) I got to get dressed and go into work - Means the ability to go work, as in looking for a job. 2) I got to get dressed and go to work - You already have a job and just get dressed to go there.