The extra cortisol could have affected your thyroid, making it hypo. Are you also balancing your hormones with Thyroxine? Did you have a T4 level on your lab results?
Frankly, you need to see an endo, and get tapered off the pred in a longer wean.
Also, the wean is going to be painful - it will hurt, so realize that up front, but it will be worth it, but since you have been on steroids long term, you have to get your adrenals tested to find out if they will tolerate the wean or if you are going to be on steroids the rest of your life. 20mg is a huge dose. 5mg is a suppressive dose so your adrenals are completely replaced and on vacation so it will not be until you get to 5 where you will try to wake those puppies up.
Pred will effect the sodium and potassium - but usually it goes high but I do tank in K as well. However one just stress doses for a short time, not for a long time. If you were not having symptoms of a crisis, she should have upped your mineralcorticoids and salt, and that would have balanced your K without subjecting you to so much steroid!
You will need an emergency kit as well - and I would ask for HC to help taper down as it is much easier.
Get an endo to test the adrenals first!
It was prednisone and inhaled steroids (for asthma) that gave me adrenal fatigue. That resulted in anxiety and panic attacks. (I got off that poison and now take natural supplements which work a lot better than that other stuff did.) If your adrenals are affected then it is possible that your thyroid is too. That can cause a low body temperature and a sensitivity to cold.