Try some free amp sims. There are gobs of them available. Run them in parallel and experiment with compression and EQ before and after the sim. One trick is to boost the midrange from ~1 kHz to ~4 KHz, distort, and then cut the same frequencies by the same amount. Crush the sh*t out of it and you can get a kind of Green Day type crunch.

WHAT!  
 
This rock star's vox samples are quite superb, imho.  I wouldn't hurt these nor refer to the talent as un-beautiful.  This vox is to die for and to bless God for.  (Yes, I've sung with many here and know you are rock solid, to my ears.  I don't think I myself or any of us sings 'Robert Plant' better than you ... TBH, all of us rockers should envy your excellent groaning.)
 
Simple vox OVERDUBS (by you, the original vocalist, else another passionate backing vox (or 2) ... increased vocal compression, vocal plate verbs, and vocal Haas delays might thicken this snappy, textural, and awesome 'Robert-Plant-like groaning' perfectly ... to be what it is, solid and true.
 
I don't think Robert Plant would benefit from too much melodyne, since he's so spaced-out and passionate about love and heartbreak calamities of his life anyway.  Your groaning needs some thickening is all ... and that snappy raw groaning takes precedence over melodic polish ... in this song at least.
 
But jmo/imho.

Your voice is fine, in fact I'd say very good.  Perhaps try a little less hard (AKA relax a bit more).

Sing at an angle up into the mic to help open & relax the throat and its 'singing bits'*.  Make sure your throat is warm (some hot honey and lemon perhaps) and steer clear of phlegm/mucus producing foods for a couple days before recording (i.e. dairy and wheat products).

Listening to yourself is a bit like seeing yourself in a photo; you finally see** how others see you, not how you usually see yourself, so it's always a bit weird; your visual mirror image has its nose pulled out through the back of your head***, and your own voice is highly modified by your bony sound-box (skull).
 
I thought originally this thread was for advice on how to treat a vocal part to make it ugly (e.g. lo-fi, bit-reduction type stuff) :-)

* - a medical term
** - see meaning hear, or see, or both
*** - mirrors do NOT reverse left and right