For testing, you can always request it through your local school district, if you can find a good reason. A few districts may consider testing for early admission to k or 1st. Otherwise probably most likely to be approved if you suspect a 2e, as you will need to state an area of concern to get a comprehensive eval done. For private testing, try this list on the website of the SAGE school in Foxboro:
http://www.sageschool.org/admission/testing-locations/Or this list on the website of ACERA school in Winchester:
http://aceraschool.org/admissions/to-apply/assessment/For all the dirt on Haverhill, see the latest coordinated program review by the state (emphasis on special education): links to current CPRs for all PS districts in MA:
http://www.doe.mass.edu/pqa/review/cpr/reports/Or this wider-ranging report from 2010: google haverhill public schools level 3 review report, and it will be the first entry (pdf)
Unfortunately, it's not pretty.
There are also some charter schools in the area. Check the DOE website for brief summaries.
http://profiles.doe.mass.edu/
