The sun is expected to increase its brightness by a factor of about 2.1 over the first 9 billion years of its life. Using extremely rough measurements, that works out to about 1% brightness every 100 million years. The Earth might be a bit hotter, in complex ways that probably depend a lot more on what we did with all that carbon and whether we humans are still around, but visually, the sun will be about the same.
Over the last hundreds of millions of years, the moon has receded from the Earth at 22 mm per year. Over 100 million years, that works out to
2200 kilometers. Since the Moon's current orbit is 385,000 km, that is a bit less that 1% farther away. If the Earth still has oceans, tides won't be affected much, and the moon will be slightly smaller in the sky. The moon is also causing the day to lengthen by about 12 microseconds per year, which works out to days that are around 20 min longer in 100 million years.
I haven't found any software that will let you look that far into the future at the constellations. However, the sky would be mostly unrecognizable even a few thousand years into the future, so on the timescale of millions of years we can expect the sky to be much different. For example, many of the brightest stars will no longer exist (Betelgeuse, for example, should supernova within the next few hundred thousand years and Rigel within the next few million years).