The blow test thing you're describing is a peak flow meter, and providing you're using the correct technique, your score isn't actually that bad (my worst patients hit around 120 on a good day). The doctor probably wants to send you for spirometry tests, which will measure how much air you can expel from your lungs over a 6 second period, and compare to someone else of your age, height, sex and weight . This can be indicative of obstructive or restrictive disease.
If you are prone to recurrent chest infections, perhaps next time persuade your doctor that you may need a sputum cuture doing, so at least you can be sure you are being treated with the right antibiotics.
Can't tell you how long a waiting list is, as they are different in different areas, but do you not have an asthma nurse linked to your practice with the ability to perform spirometry?