What sort of exercises are you doing? I mean for example it looks like you're training full body, which I assume includes legs, the day after leg day... So yeah that might not be ideal, as rest periods are crucial to muscle development, but it really depends on what you mean by "full body." like, I would go run a treadmill the day after leg day...

Are you going to a gym? Lifting weights? Or home? Bodyweight workouts? Cardio?

I have a couple ideas but real quick just gonna say that as long as you're giving each body part a rest, for example not working arms two days in a row, that's prob ok.

Ok i have a little more time now, just some thoughts :
First, just to put it out there, Im no expert.  I just read a lot of crap and have been working out for a little while.  I started with bodyweight, then joined a gym. Most of what I know about splits is from aworkoutroutine.com. I would suggest checking it out.  It’s a really straightforward site.  He deals mostly in weight lifting, but I think you could still benefit from some of the concepts, especially regarding beginners and how they benefit from big compound exercises.

I used his “beginner weight training routine” at the gym for most of the past year and it’s great.

You could, if interested, probably adopt a lot of the concepts and structure behind that workout and come up with an intelligently designed home bodyweight workout.  
Backpack/weighted pushups subbed for bench press for example
Googling gave me a ton of results about pushup variations.

The only equipment I really think is necessary is a pullup bar. Pullups are so awesome.
If you don’t have a pullup bar I would recommend finding one outside, finding a way to improvise one, or just get one.  I used to do bodyweight exercises in my apt complex playground, with a backpack on with weight.  Simple routine of pullups, inverted rows, and dips, twice a week. That was pretty much my complete upper body routine, with minor attempts at variations.  Big compound exercises and I saw some results.  Pullups are so crucial.  These days I would probably do more pushups than dips with what I know now, but it was good. 

Anyway, definitely use google, like just now I googled “bodyweight alternative deadlift” and got a bunch of results that i had no idea existed….

Without weight you can of course do bodyweight squats with variations, then for more muscle challenge, try pistols (one legged)  A good way to practice them is on a stool or something.  Allowing your leg room to hang gives more stability.  They’re wicked.
Google is your friend.  I just googled “bodyweight muscle split” to see what I could find and the first site offers something like “the ultimate bodyweight routine” and some of the info in the beginning seemed ok but then I got tired of scrolling past things they were trying to sell and never got the the actual ultimate routine.  But there were a lot of results and I'm sure there are tons of ideas and variations you can find to really work around the limitations of not having weights and still getting max benefits.

That's about it, just some ideas. I'm sure whatever you come up with will be fine. Especially if you continue to explore and read and adapt. Good luck!

I suppose you could always split body parts into different days

Eg: Back
      Legs n glutes
      Chest
      Arms
      Shoulders
      Cardio n abs
      Rest
I mean thats what I'd do if i was able to go for 6 days at the gym.