One can turn off all the symmetries in the ED solver or solve for all the symmetry sectors separately. It is definitely better to utilize the symmetries (at least momentum and/or local symmetries) if they are conserved. Therefore, while it depends on the kind of problem you are interested in, I suggest to do ED in each sector and then collect the eigenvectors if needed.
As a side note:
I do suggest that you implement a simple ED code with your programming language of choice. Doing so might be a bit slow but does give you a lot of intuition into how these computations work, teaches you more about the physics, and also simplifies your way to make use of better written, more reviewed, and faster code (such as the ones implemented in ALPS) much more efficiently.
Honestly, starting from scratch, with no prior experience it should not take you more than a few days. Happy coding :)