There are a variety of strategies to repel insects which people swear by. None listed contain DEET. Each of these comes recommended!
Internal repellents for mosquitoes:
Eating lots of garlic or taking apple cider vinegar
External repellents for rubbing on your skin:
Apple cider vinegar or garlic
Oils such as citronella, tea tree, peppermint, almond, and jujuba `– Make your own mix!
Oil of lemon eucalyptus (OLE) is recommended by the Center for Disease Control
Cedar oil is useful for ticks.
For itching (in case you do get bitten):
Ice, which will also decrease swelling
Pastes made of baking soda or oatmeal