How Can Cough Along With Wheezing And Breathing Difficulty Be Treated?

I m a 35 year old female who had a cold at the end of june which turned into a cough and wheezing (I went to one doctor who advised to get an inhaler which helped slightly) and then I became breathless around end of July to the extent that when I walked up stairs I was really out of breath and my muscles in my thighs hurt. Even getting dressed in the morning was sore on my legs and arms, the pain felt like I had been exercising the day before. I went to the doctor who sounded my lungs and said it sounded like my left lung wasn t filling properly, an x-ray didn t show anything wrong so they gave me antibiotics for an infection which did help but didn t completely go away. I then went to Hawaii for 10 days from 21st Aug and whilst away I only had to use the inhaler once. Since returning to Melbourne the breathlessness, cough and wheezing has flared up again and I went back to the doctor on Monday who advised she could hear wheezing in both my lungs and advised I probably have asthma. She prescribed a low dose inhaler (this one has steroids where the other one didn t) and was asked to take two puffs twice a day and go back in a week to see how I m getting on. I still feel slightly breathless and if I take a deep breath I get a weird sensation across the bottom of chest, not really painful but kind of feels like the air isn t quite filling up my lungs. Should I need further tests to prove it s asthma and does this sound like I have asthma. I should also mention that I m allergic to dust mites and slightly to cats and dogs (I have 2 cats and 1 dog who have never really bothered me with allergies, I could normally take an antihistamine and be ok) The doctor said when I did the allergy test about 3 years ago that because I was really allergic to dust the cats and dog wouldn t even bother me. Just want to see if you recommend any further tests. Thanks Carrie