To add to this, it may get stalled by the Records Access Officer if an investigation is open if you go the Public Records Route. Under Exemption (f), law enforcement can redact or withhold records subject to an ongoing investigation. The public records law does not give anyone a superior right of access to a public record even if you’re the person who would be the beneficiary of the investigation. So exemption (f) still would apply to OP. Just something to be aware of

If you’re open to going anywhere in MA they can place you within a couple of weeks. Regulations say they need to place you immediately

I believe EA shelter is open to folks regardless of citizenship status. You just need to prove MA residency (I.e. driver’s license)

If your income limit is 115% or lower of the Federal Poverty Level ($1,775 per month for household of 2) you may qualify for EA shelter. If you don’t believe DTA is helpful, is it because they aren’t really getting back to you or they’ve determined that you’re ineligible? If it’s the former, I get it’s frustrating, but if you hound them they have to respond eventually