It sounds like you might have a Cucumber Beetle or Squash Bug problem…common for them.

Here are some links that might help you pin down the exact issue:

http://www.clemson.edu/extension/hgic/pests/plant_pests/veg_fruit/hgic2207.html

http://www.almanac.com/pest/squash-bugs

I suspect squash bugs from your description.  A combination of Pyrethrin (contact killer) and Neem Oil (stops larvae from feeding and maturing) would do the trick. 

Follow the directions on the label. 

http://www.bonide.com/products/insect-and-disease-control/view/026/bon-neem-ii-conc

Here’s the label.

http://www.bonide.com/assets/Products/Labels/l026.pdf