You cannot recycle hand towels or paper towels.
Paper towels and hand towels are not recyclable and should simply be composted or thrown out in the trash.
However some places may accept used cloth hand towels and use them for rags such as in a shop or they may sell them to a shop.
My place has a recycling center that employs disabled people and they accept cloth hand towels and rags and then they sort them and place them in a bag and sell them to places like automotive shops who use them for grease and oil.
Many places don't have places though that are setup to recycle cloth hand towels.
And paper towels are currently not recyclable and should be thrown out.
If you do put any cloth towels or paper towels in a recycle bin they most likely will be thrown out during the recycling process.
The cardboard roll in the paper towels and toilet paper rolls themselves are recyclable as they are cardboard.
If you have some towels and sheets that are still in decent condition and want to get rid of them, you can consider donating them to local shelters, animal rescues, or thrift stores.
Many organizations appreciate bedding for their clients or animals.