I have a 96’ Blazer and when I turn the turn signal on to the right it functions as it should, but when I go to turn on the left turn signal it will blow my turn signal fuse after the first click. I replaced the relay under the dash and it’s still doing the same thing. I recently replaced my headlights for new LED ones, I’m unsure if a melted or pinched wire would cause the issue with my turn signals? Any advice would be appreciated greatly

 

Yes this could and will cause that issue.
Trace the left turn signal wires down.
Perhaps in an area where previous work or collision damage may have occurred if any causing a pinched wire or near a area where the wires are subjected to extreme heat causing them to be melted and exposed to one another.
Check grounds aswell as I am facing a similar issue but with a fuel injector causing my 15 amp ecm fuse to blow.
Did the issue happen before replacing your headlights?
If not I'd check the left headlight.
Or possibly the headlights themselves could be the issue. Especially if they are cheap knockoffs from China or somewhere (meaning they weren't built with quality parts or craftsmanship)
I had a nissan that I placed LED bulbs from China off of ebay in my tail lights and caused a whole issue with my brake system.. (don't ask me how. I'll have to dig up an old post from that forum)