Ordering the elements in a list and separate them into sublists for plotting

I want to plot the following data:

 y={{0., 2.14557}, {0.1, 2.14589}, {0.2, 2.14686}, {0.3, 2.14852}, {0.4, 
  2.15092}, {0.5, 2.15415}, {0.6, 2.15834}, {0.7, 2.16363}, {0.8, 
  2.17025}, {0.9, 2.17844}, {1., 2.1885}, {1.1, 2.20076}, {1.2, 
  2.10506}, {1.3, 2.11519}, {1.4, 2.12737}, {1.5, 2.14122}, {1.6, 
  2.15726}, {1.7, 2.17674}, {1.8, 2.2012}, {1.9, 2.10502}, {2., 
  2.13057}, {2.1, 2.28359}, {2.2, 2.18106}, {1.2, 2.21549}, {1.3, 
  2.23277}, {1.4, 2.25188}, {1.5, 2.27083}, {1.9, 2.23041}, {2., 

  2.26034}, {2.1, 2.28359}}

I was thinking of plotting the data with ListLinePlot, so I have something like:

I tried to order it into three different lists, like

y = {{list1}, {list2}, {list3}}

where list1 corresponds to the first plotted line, list2 to the second and list3 to the third, so it would be easier to separate them and plot them. However, I couldn't do it successfully.

How can I achieve this? Is there a more intelligent/convinient way to plot the list y?