Is it a historical novel? In this day and age, it would be pretty unlikely for a family to get trapped in their home by a fire, unless they were asleep in bed, on the second story, where they can't go out the window without risking death by falling. Or in an upper level apartment. Most houses have smoke detectors that go off, giving you at least a minute or two to get out before you're in danger.
For sensing a fire, unless you were in the same room, you'd probably smell the smoke first. You might hear the crackling of the flames, if you were near enough. If the fire was on the other side of a wall or door, the surface might be hot to the touch. That's why they say don't open a door without feeling it first. You might open it and discover an inferno on the other side.
Generally speaking, the poison gases in the smoke will kill you long before the fire does, if you're trapped and there's no fresh air. It's my understanding that more people die of smoke inhalation than from being burned to death.
If you're burned, it's going to hurt like hell. They say it's the worst pain a human can experience. There are different stages of burns: first degree, which is where the skin is reddened, like a sunburn. Second degree has the skin blister. Third degree, I believe, is where the skin is actually charred. Most hospitals have special burn wards, where they care for burn victims. Some burn victims need special frames on their beds that keep the sheets and blankets from touching them, because it would be too painful. They might require skin grafts to replaced burned skin. If extremities are burned badly enough, they might be amputated. You can Google this kind of stuff, just be careful--you might find graphic images.
Just a guess, but being rescued probably wouldn't feel like much of anything, at first. You would be running on adrenaline, trying to find a way out, trying to save yourself. Then someone saves you. You might feel numb at first. In a daze. Maybe even confused. The emotional impact would vary depending on the circumstances of what you'd just experienced. How close were you to dying? How afraid were you? Were you paralyzed with fear, or did you take action, ready to save yourself? Did you suffer injuries? Were you alone? Did the others with you get saved or did they perish? If you survived and they didn't, you might feel survivor's guilt. You might get angry at your rescuer for saving you instead of the others. Lots of potential for emotional impact with this.
For a personal experience, my parents' house got struck by lightning eleven years ago. It vaporized the TV antenna in the attic and started a fire in the insulation, but we didn't realize the house was on fire for several minutes. We kept smelling smoke, but we didn't know where it was coming from--not until my father went upstairs and saw smoke coming out of the air vents. He came back downstairs and we all rushed around like headless chickens trying to gather the most important things we wanted to save. I tossed a laundry bag full of books and my medications onto the lawn, and a minute later, left the house with my wedding dress over one shoulder and my baby sister in the other arm. (I was getting married in a few weeks, so saving the dress was high priority!) A minute or two before we left the house, the smoke detectors finally went off. My lungs hurt afterward from breathing in the smoke without realizing it. When we got outside, we saw flames shooting out the attic window, which sent us all into shock, even though we were safely outside. To my horror, I realized I'd left my backup disk with all my writing on it upstairs. (This was before the days of internet backup.)
It ended well, nobody got hurt, but it was a significant, life-altering event.
