getting an erection.

I would like to encourage you to not give this much concern. Although I understand you're embarasment and awkward feelings, I'm sure it's rather normal. It's just something we don't generally talk about. When was the last time anyone you knew told you he was getting erections at awkward times? I did ask friends on mine that are in the medical and massage fields, and they all said it happens, just don't get sideways about it. Your penis is simply doing what it is supposed to do. I think your 'issue' is rather better that having a penis that is so shy it practically disappears when exposed, leaving those around you feeling sorry for your wife or girlfriend. My advice, relax and wear it well...

As jorock says, this is pretty much normal, though it affects some people more than others, and may go away as you get older.  I used to know someone who worked on a ward with spinal injuries, and had to help them urinate, and she said it happened all the time.  It was mostly young men in there because of motorbike accidents, or diving in the sea and hitting a sand bar (this was in Australia), and they used to joke about how much they were enjoying it, but the sad truth was that they couldn't feel anything down there.

If you explain the potential problem beforehand, I think they'll understand.  As far as preventing it, the only thing I could suggest is, if possible, to masturbate an hour or two before you're in a difficult situation - a so-called "safety wank".  This tactic is famous from the film "There's Something about Mary".

In your position, I'd probably be embarrassed too, but I most definitely would not refuse the help on offer.