7 hours for a 3 month old is pretty good, is she getting any sleep at all during the day?
Does she feed well, or does she fall to sleep while you are feeding her?
Does she have wind/cry a lot?
When you want her to sleep during the day, what do you do? do you go to her room and turn out the lights, or are you trying to get her to go to sleep downstairs? Will she sleep if she goes in a pram or a car?
I wouldn't feel guilty about putting her in a pram, and going for a walk if that's the only way you can get her to sleep. The exercise will help you, and if you can get her back asleep you can have some time for yourself.
If she isn't crying, and she is eating, then I don't really know what a doctor would do, but I would say first and foremost trust your own instincts. I only wish I had done that with my PFB.
It might also be worth speaking to your health visitor.