Certified GKH Gardening Expert
Depending on the type of spray that you used, it could have caused the burning. Any oil based spray should be sprayed out of direct sunlight, and tested on a small area, as per packaging instructions.
Most non oil-based pesticides won't carry this same risk.
Honeysuckle are very hardy, so I suspect that they will come out of the damage just fine.
Here are some articles that will help: