Hi Andy and welcome to the forum.
There are a few things you can and maybe should do here.
Plug in surge protectors only protect your trailer from a power surge, then it's dead. You will want to move on to something a bit more advanced than that and get something that protects you and your trailer from more than just power surges. The following video link explains a lot about plug in style protection, even though the products he shows are for 50a products they also have the same units for 30a. Quite a few people on the forum use this style and prefer it, if your not comfortable hard wiring in a unit, it's definitely the way to go.
I and many in here use a hard wired variety, I'm on my second as I had a TT with a 30a service and now have a 5th wheel with the 50a service. I installed them both with much cussing and sweating but the job got done.
In regards to your cord, some folks like pulling the cord from the trailer as it is easy storage, some like to install an external outlet and store cord elsewhere in trailer. That is just personal preference. Either way, if my plug looked like it had taken some heat like yours did, I would have it replaced, not just the plug. I would also go with an outside receptacle so I could replace the cord myself if anything else happened to it.
In my opinion, if you're not comfortable working with electricity, I would have an external outlet added to trailer, buy a new cord and either a "Surge Guard" or "Progressive Industries" plug in style of electrical protection. It is truly a plug and play peace of mind while travelling and camping.
Good luck