Get a second opinion.
I have not seen hoarseness 'because of' teething.
However, my Pediatrician does not like Oragel and does not recommend it, because it can ALSO 'numb' not only the gums....but also the throat, and in some kids it will affect swallowing ability.
I would not give him so many things at one time, or overlap them. In a baby, even something seemingly harmless, can become a systemic irritant, IN CONJUNCTION with other things.
Now, he seems 'warm' to you...even though he does not register a 'fever' per say statistically. Maybe he is just running a low grade under the radar fever..... ?
I would get a 2nd opinion. It could be anything... but the thing is, his hoarse voice returned... perhaps from crying, perhaps a virus, and he broke out in a rash once. This rash can be from the Oragel, or perhaps it was a 'viral rash' which many babies get AFTER a fever and viral illness...it is the bodies way of purging the toxins from the body.
So, the rash could be anything... and has not been determined nor diagnosed.
Now, how is his ears? Is there fluid in it? Infection?
How is his sinuses? Mucous? Infection? Post nasal drip?...these things, such as post nasal drip, can cause hoarseness.... I just was sick with a head cold and got laryngitis from the post nasal drip, along with a low fever.
No, I would say that this is NOT DUE to growing... he sounds ill... or there is some kind of reaction in him, negatively, from all that stuff he ingested for his 'teething.'
You have to see a Doctor, or take him to the ER for further diagnoses. He is just a baby... you don't want it to go on and on and on... and keep wondering. Find a conclusion to this. And don't keep guessing and keep giving him over the counter remedies, unless you know for certain that it IS teething, exactly.
Or, perhaps, sometimes when teething, extra saliva gets excreted...and swallowed. I don't know if this is a possible 'cause' of his hoarseness. But I have never heard of teething causing this.
Also, if he is getting up at night, no matter how many times... certainly console him, nurse/feed him, and help him feel better. If he is hungry, he is hungry and needs a feeding. Don't deny him this.
All the best,