Kelly, hi & welcome. I'm just a patient, so please read in that light!
I couldn't tell from your post what tests your doctors have run, or whether you've seen specialists (rheumatologists, hematologists, etc.). Usually when ANA persists at that high a level, *more specialized tests* are run to investigate the multiple conditions in which ANA elevates. Ditto for persistent anemia, to find out what type of anemia it is. I believe specialists, not GP's, tend to be better at such "fine-tuning".
STARTING WITH WHAT YOU WROTE. I don't know if ANA elevates in asthma (sorry). I think it can in pernicious anemia, but I don't know whether your anemia was ever narrowed down to a specific type/cause? ( BTW, I also had anemia on & off, the B-12 kind, which I've read is common in multiple inflammatory conditions, including lupus.)
RE DIAGNOSING LUPUS. Have you seen the 11 diagnostic criteria in the "sticky posts" at the top of the thread list? You generally have to meet at least 4 of the 11 to support a Dx of systemic lupus. And not necessarily all at once, meaning you can meet them over time: think of checking each off, once met, in indelible ink. To know if lupus is in the ballpark, drs run more specific tests looking for specific autoantibodies: anti-ds-DNA, anti-Sm, anti-Ro, anti-La, RF, antiphospholipid, etc. (There are a bunch!)
SYMPTOMS. I believe it's possible to have lupus with only a FEW symptoms IF lupus is proven by the specialized tests that qualify as "criteria". So if lupus is a possibility, but you haven't all the tests that appear in the criteria, you should! (I actually had many more "symptoms" over many years, but my drs. weren't thinking lupus & thus didn't look to see if I met those criteria.)
Another thought might be rheumatoid arthritis (RA), and I imagine there are other possibilities, too... Anyway, I'm sorry you're having problems & hope that your doctors and you keep trying. I hope you post more soon! Meanwhile, best wishes, sincerely, Vee