Well, low estrogen and vag. dryness are pretty common while nursing and I am very surprised that you were prescribed Estring. Not only can it interfere with lactation (did the nurse know that you were nursing and planned on keeping on doing it?) but if you do get your estrogen level up artificially, you may increase the estrogen level in your milk and such pass it on to your son. That can have all kinds of unwanted side effects like breast development. The patient information states pretty clearly that it is contraindicated if you are nursing. That however is the case for any estrogen preparations, now matter if it is a ring or cream.
While you are nursing the best way is to stick to lubricants. You may get back to normal naturally after weaning or can get properly diagnosed at that point - if your doctor hasn't done so yet, also get your thyroid checked (that can be done now)!
BTW, I have a mirena too, and do very well with it. It did not affect my milk supply at all (nursed until 19 mo) and have no side effects whatsoever - but every woman reacts differently to it, so keep that in mind...
Good Luck!