My daughter has both as well. She was tested at around 9 mos. due to severe eczema. My husband had given her peanut butter on toast after we found out - don't ask. She reacted immediately. Thank God we didn't need to use the epi-pen because of it. She was tested again and the dr. said they have learned that kids can grow out of that allergy. He has said that her test was abnormal but not highly abnormal so there was a chance. Unfortunately, hers became worse. Her doctor also confirmed it with blood work. THe AMA stops measuring peanut allergy at 100 (in blood work) and she is 100. Coupled with asthma it is a dangerous combination. Go for a second opinion and ask that it be confirmed with blood work.
My daughter's allergy doctor put her on the albuterol after several bouts with ashtma. And after that he put her on another daily medication. She had her tonsils out 1 year ago and her ashtma has improved so much she does not take the daily preventative any longer. She needs something in the spring and the fall. Pay attention to when your child gets these "colds" because it could very well be seasonal.
Definitely get a second opinion. There is nothing to lose and lots to gain by doing it. Make sure that they are familiar with pediatics. My daughter's doctor is in my local area but on staff at Children's Hospital so it gives me a little more comfort.
If you need anything further, please email me.