My DS had a DODMERB DQ for asthma, and eventually received a waiver and appointment, but it was a VERY complicated road to go down, and the odds of success are not high.
Before you send ANY documentation to DODMERB, you need to research and understand the DODMERB standards and ensure that you are not creating problems that could be avoided. Only answer the questions that are asked, do not provide any extra info, and make sure you understand the standards:
https://www.med.navy.mil/sites/nmotc/nami/arwg/Documents/WaiverGuide/DODI_6130.03_JUL12.pdf
Getting a letter from a doctor "clearing candidate for military service" is not useful at all. Only the military clears candidates. They are only interested in receiving descriptions of conditions and diagnosis from civilian doctors, then DODMERB and SA make a judgement. So, the important thing to do is to understand the standards, and help the civilian doctor understand the standards, so that the doctor can provide documentation that the candidate does in fact meet the standards - if that is what the facts support.
If you already have medical records that include a definitive diagnosis of Asthma, after age 13, (mild, exercise induce, or whatever) you will certainly get a DQ. There is no grey area.
However, you CAN get a waiver, but you need to be proactive. In our DS case, the diagnosis was based on a few episodes of wheezing and shortness of breath during exertion. There are many possible causes, but the doctor put "likely exercise induced asthma" in the record - automatic DW.
At the time, we knew that would be a DQ, so we took son to a pulmonologyst. He underwent a PFT, which showed normal, and we even got the doc to do a methocholine challenge test, which was also normal. We showed the DODMERB standards to the doc, so that he could make sure he used the right terminology to leave no doubt that there was in fact no asthma. He also wrote a letter stating his opinion very clearly that DS 'did not have asthma' and summarized the data to back that up.
All of that info was provided when DODMERB requested remedial info, and DS still got DQ'd. After the DQ, we went to another pulmonolgyst and got a second opinion that said the same thing as the first. After many months, DS eventually got a waiver, but it was far from certain.
best of luck