Alm or Eirika refine?

Alm, he will serve you better. Eirika still needs to be in a mixed tactic team to be her best

Well Eirika is the more easily merged unit, so she has a more realistic max potential (unless of course you are willing to invest a lot of money). She's also great if you run an infantry blade tome user on your main team.

But for a single merge unit, I think Alm would be the better choice, given how prolific dragons are in the current meta.

this man has never lost to any dragon, even a 10+ nowi.

Between these two it kind of depends on your playstyle tbh but with those Alm IVs? Definitely Alm. Slap on DB3 and most everything will die before they can get an attack off, assuming you'll be using a dancer and/or a healer. Eirika's refine takes a little more teamwork and strategy but is still very good.
If you're patient you can probably get both refines by the end of the month depending on the rewards you get so I wouldn't worry too much about it (maybe a month and a half). But in my opinion Alm takes priority