Alimony and my rights.

Alimony is not primarily about compensation for what you did in the past: it is about providing support for a former spouse, on either a temporary (few years) or permanent basis, based on multiple factors, such as: your earning potential; your other sources of support (e.g. from a committed, live-in relationship, or family money/trusts, if any); how much your former spouse earns; the lifestyle you and your former spouse enjoyed (the court tries to not let your lifestyle fall too much below what it had been, when feasible).
Being in a supportive relationship, living with someone who supports you, is a significant factor, but not the only one. It will weigh in the decision as to whether to grant you alimony, how much, and for how long, but does not automatically make you ineligible (the way remarriage would--since you and he are not married, he does not have a legal obligation to you, and that is something ther court will weigh). If your live-in earns more or less what your former husband did, so you are living a similar lifestyle, that reduces the odds of alimony; if your former spouse earned much more than you current significant other, so that your lifestyle now is much less than it had been, the weighs in your favor.
Ask for alimony, and your attorney should be *aggressively* advocating for you, not simply advising you that you won't get any. While its possible that under these circumstances, you will not get any, it is also possible you will get at least some, and on at least a temporary basis. Since any money is better than none, seek alimony and don't give up.