Addressing the issues one by one:
People that were previously very friendly are increasingly becoming distant
If you were promoted and there are underlying issues with management, this happens. While you were "in the trenches" before, your colleagues might now see you as the very enemy you were fighting.
People are complaining and frustrated about decisions not made by me but senior management, yet taking it out on me
Well, this is your job as manager. Take the grievances passed to you by your direct reports and collate them for your own management. Failure to do this results in resentment from your staff.
Social events are awkward and uncomfortable to the point I no longer want to attend them
See first and second points. If your staff feel like you are not on their side, they will grow to resent you.
You don't have to be best friends, but you do need to represent their interests to your superiors.
Gone from a position of being highly valued to constantly feeling like I need to prove my worth to management and people in general. It seems like no matter how hard I work, it is not the same value as other individuals doing equivalent work who get recognised.
It's not always about performance, but about perception. You've said that your staff are becoming less amicable, and this kind of thing gets around. Your superiors might see fantastic results, but are probably hearing gripes and grumbles, which undermines all that you are achieving.
So, how to progress?
Get on a management course, either through your company or through a third party. This will help to highlight the areas of your management style that need improvement, and reinforce the parts that are already good.
Make sure you have regular meetings with your whole team where you can pass down management instructions and they can feed back openly. It doesn't have to be a long meeting, just 15 mins a week should be enough.
Stop trying to shoulder all the burden. Complaints from your staff might be completely valid, or entirely baseless. Sort the wheat from the chaff and pass along important issues to your superiors as soon as you become aware. Let your staff know when you do this, and chase your own bosses for answers if they fail to reply in a reasonable time frame.