You can buy flush ceiling fans. Should be fine as long as it's over furniture, such as the bed.

There are "flush mount" or "hugger" fans for low ceilings. The motor mount of such fans is directly below the ceiling. There is no downrod. Examples:

• Modern Fan Company
• Monte Carlo Fans

I bought the Monte Carlo Clarity 42 which works well though the light from the integrated LED is rather harsh. The fan is very quiet, can be reversed from the remote control, and I liked the feature that allows you to replace a wall switch with the remote (it doesn't actually use any of the in-wall wires) or embed the remote in a small case (supplied).

Be sure to properly size the fan to your room's dimensions.

Warning: Be sure the fan's light is shaded from the fan blades. I bought this Fanimation Studio Collection LP8577LMW for my dining room which has lights on top and bottom. However both lights shine through the fan blades creating spinning shadows around the room whenever either light (or both) and fan are on. As a result, the fan is really unusable when either light is on. The Monte Carlo fan has a shroud around the light so it does not shine through the blades.

On build.com, they call this style “hugger” fans. I would still measure to make sure it will not be too imposing.

https://www.build.com/all-ceiling-fans/c108543?f57658=hugger&r=48&s=SCORE&p=1&categoryId=108543

Minka Aire makes the best hugger fans and just recently introduced their new and improved Concept III Flush Mount Fan that is available in White, Black and Brushed Nickel

Been selling fans for almost 30 years and this is one of the best flush mounts I have seen on the market. Has a super efficient DC motor with a 6 speed remote. Runs dead quiet, which is perfect for bedrooms.