Yes, keep breastfeeding. As well as providing antibodies for your DS, breastmilk will help to keep him hydrated. If he does manage to keep any down, even for a few minutes, breastmilk is extremely nutritious and is a perfectly balanced food. And of course breastfeeding can be ever so comforting for a poorly wee mite.
When DS was 14 months old, he had a horrendous tummy bug which went on for about a fortnight. Breastmilk was the only thing he could keep down. The GP prescribed him a foul-tasting electrolyte drink to prevent him from becoming dehydrated, but also said not to worry if DS wouldn't drink it as breastmilk was doing the same job only rather better. He added that if DS had not still been breastfeeding, he would probably have ended up in hospital on a drip.
Hope your little one starts to feel better very soon.
Your milk will be helping him, not hurting. You will have been exposed to the bug, and be putting antibodies to it in your milk. I wouldn't stop breastfeeding. (Current best practice, afaik, isn't to limit adults to water, when they have a tummy bug.)
My 10 month old son started with this sickness and diarrhoea bug a week ago. He is on solids but I still breastfeed him. We ended up on hospital Tuesday night as his temperature was so high and he needed rehydrating. Then, just as I thought he was recovering we end up back at the dr on Thursday as he now has an ear infection. He was given antibiotics but 24 hours later he was vomiting again. Back at dr yesterday and he is off the antibiotics but He is still throwing up (a lot) so I am considering stopping the breastmilk for 12 hours and just giving water. Should I?