It sounds to me like you need a new doctor that will take your concerns seriously. Have you told your doctor that this doesn't feel like asthma has felt to you in the past? There are oodles of problems that can cause that chest tightness. One thing you can do is ask your doctor's office to give you a lab slip for basic blood work and make sure they test your iron stores (i.e., ferritin) along with the CMP and CBC. Low iron can be a cause of this and it's far more common than folks think. It's the iron in the red blood cells that helps to transport oxygen through your body. If you can get your blood work done ahead of the appt, then the doctor has something to work with. You can also get blood work done on your own. This company sends you a lab slip that you can just take to any Labcorp office: www.healthcheckusa.com
Low magnesium and calcium can also contribute to the problem - the magnesium in particular with regards to the chest tightness. As an FYI, the majority of americans have low levels of magnesium and it can be made worse if you take calcium supplements as that binds with the magnesium.
Most ERs are fairly chaotic and honestly if you go in and tell them that your doctor says it is just asthma, while they will do due diligence, there is no magic in terms of them figuring out what is wrong any better than a good doctor. And, indeed a good PCP should be putting together other pieces of information from your past to figure out what is going on.
I do share your concerns as I also have asthma and have periods of severe shortness of breath that are inexplicable to me - i.e., they don't necessarily seem to correlate with other asthma related issues. I have other odd symptoms that point to something else going on. But, I trust my doctor and this is something I'll discuss with her at my next appt - and I already have a lab slip so she will have the most recent test results. I always get one at my previous appt and have the labs run a couple weeks before my next appt - that really optimizes my time with the doctor AND it really speeds up treatment.