Firstly, it's not you or anything you're doing. You're not "too wet", so stop worrying about that.
If he's physically fit and healthy, I'd put my money on this being a psychological issue, especially if he can cum from oral or a handjob. He knows there's a problem with penetrative sex and, the more he thinks about it, the more he'll struggle to maintain an erection. As a PP said, it's a vicious circle.
It's understandable that you don't want to make him even more self-conscious but you need to have a conversation about it. Avoiding sex is not the answer and you'll both just end up frustrated and resentful.
I'd check how often he is masturbating and whether he's watching a lot of porn as that may be a factor. If so, ask him to stop or reduce it for a few weeks.
The redness and soreness is worrying though and I'm surprised he'd tell you at the start of the relationship that this is the reason he can't perform a second time. If he won't go to the gp, would he go to a sexual health clinic..? You could suggest you both go for tests and an annual "MOT"..?
Regardless of whether he loses his erection, you sound very unfulfilled. What is he doing to make you cum? At the very least he should be making an effort to please you too. If he's just having a quick shag with a semi and then rolling over to sleep, you need to set him right!