Pediatrics and asthma

Patient: My daughter has not yet Been diagnosed with asthma my childs pedoatrician has given her an inhaler on which she has became dependant in and can not go with out weezing for 4 hours stright. When she runs she begins to weeze and we have had 2 cats fir a couple of years and she has just strted wheezing, and she is usually very active and can go without weezing and she is very fit and enjoys playing with her sisters. She is not over weight or unfit but it eorries me should i continue to let her play outside and run aroundnher house. She is only 5 and my doctor does not want to refer her to an allergist yet he wants to wait but i am very worried and about to change pediatricians