There is only one way to get fitter:
Exercise.
That's it, no magic, no other options. Just exercise. The more you do, the fitter you'll get.
Losing weight is great and commendable, but just dieting won't make you fitter, it'll just make you lighter.
The best thing would be to do both - lose weight
and exercise. Handily, they compliment each other fantastically.
Walking is ok exercise to begin with, if you can't handle more intensity - but you need to push yourself to see any change.
(Seek specific medical advice before starting a new exercise regime, ask the question about it directly - I can't be held responsible for heart attacks
)