Its probably took years to become unfit and sadly you do not become fit over night, but your going in the right direction. A lot of smokers have the attitude that when they stop, there body will be OK, but sadly that is not the case the damage is done and it takes hard determination to get fit again, so well done for taking the plunge
I've had an on and off relationship with cycling for years but almost two years ago I have took to it big style for the last time just to keep fit but mainly to keep my weight down and determined to keep it going till they bury me now.
Looking at my records from 12 months ago, I was stopping seven times on one hill for breaks of up to two minutes to get my wind as my lungs would be bursting and also let my heart rate drop back down and I was crawling up it at between 1 to 4mph. Yesterday I went out and did it 5 times on the trot, with no stops and cut my time down from 20+ minutes to just over 7 minutes a climb, the day before I had done it 4 times so in 12 months I have come a long way but it was through perseverance and not giving up.
Do not worry so much about stopping, it will be inevitable at first, if you feel embarased about stopping, look purposeful as to what you are doing instead of looking like some thing that just crawled back out of a grave and needs putting back in it, my favourite on very steep hills would be to stand upright off the bike looking back down as if your waiting for others to catch you up. Find your self a ride that you can manage with a push, record everything you do, look for the slight improvements as time goes on as that is what will motivate you, and in 12 months try the same ride again and see how much you will have improved.
As Garz suggests though it may be worthwhile seeing the doctor just to confirm you are OK, as 3 miles is not really that far to be suffering as much as you are.