Your doctor is probably right. It is well known (British Association of Riding Schools) that older people are better taught on horses that are not too wide in the barrel.
I cant ride cob type horses. But it is not just width, it is the shape of the horses back - a wide flat back makes things worse. You may well be in pain after riding a broad backed cob. I always am. Both my lower back and left hip.
One riding school much recommended on NR turned me away as a dressage student recently because they didn't have a suitable horse. They taught mostly on cobs.
I started riding age 62 with a bad (degenerated) lower back which affects the nerves to one's lower body, especially my left hip and leg. Not the same as your hip problem but not so different. Left hip hurts most of the time.
The first riding school I went to taught me on a nice cob on which I habitually sat crooked, that is on the diagonal, with my right leg farther forward than the left. Most of us older people find it easier to take a long stride forward than to stretch our legs apart sideways. So if we are given a horse too wide for us, that is how our body adapts.
Next time you get on the horse have a look at your straightness - in every direction. Are you upright? Are you centred on the centre line of the horse from from to back? And are you sitting at right angles across the horse's centre line?
At my second riding school, a senior RI made them switch me from an Exmoor pony to a horse of 16.01 hands on which I did much of my learning to ride. The RI also ordered the staff to lengthen my stirrups. This could help you too. It puts more weight on your seat bones and less pressure on your hips.
It is a great nuisance not being able to ride cobs or wider horses, because it rules out so many otherwise suitable ones. But I am in pain after trying such horses and have learned to be firm about it.
The good side is that I do ride comfortably on some big horses. eml taught me on a horse of 17 hands and last week at another school, I was put on another.
A lot depends on the individual horse. If you are looking for a narrower pony, the love of my life is a Connemara cross. My cousin's Welsh pony, also looks rideable by me - but her Dales is too wide.
I cant advise you on the saddle. I have been fine in Western saddles, but my only hack in a treeless, (and on a mare too wide for my liking) like you I was in pain next day.
I hope this helps. I don't find it easy myself. because sometimes I can see a horse is too wide, sometimes, I need to get on and try, and sometimes I force myself to ride because a school wants me to, and then like you I am in bad pain. My standard is to say that if I am in such pain that I cant sleep properly at night, then I wont ride that horse again.
But moderation is also a factor. If you want to keep your Exmoor pony, you could consider the amount of riding you do and limit the time you spend in the saddle? I suffer if I canter in sitting seat too much, it is best to take a day's break before riding again? If I hack fast on four consecutive days or ride for two hours, I am worse off? So if you are riding endurance, I probably couldn't do that, regardless of the horse.
My slender TB and my friend's Arab x are not so bad, so I do think that if you suffer with hip pain, the width of your horse can be a contributing factor. 
