When exactly in spring did you notice this - at the end of March or already in April when the thaws started?
Your neighbor is partly right, but it's not quite sunscald in the classic sense. Most likely it's temperature fluctuations: during the day when it thaws, the bark warms up and starts to "wake up," but at night the frost kills it. This hits hardest at branch forks, where the bark is thinner and less protected. The blackening is dead tissue, and the swelling shows that decomposition has already started under the bark.
As for saving them - damaged branches usually can't be saved. If the blackening is only on the bark, you can clean away the dead part in spring and disinfect the cut, but if the wood under the bark is black, the branch is already dead. Cut it off flush with the trunk so it doesn't get in the way. Going forward, the main thing is to prevent sharp temperature swings. Whitewashing the trunks and thick branches in fall before the first frosts helps: the paint reflects the sun and keeps the bark from warming up during the day. Wrapping young trees with non-woven fabric also makes sense. Also try to pick a planting spot so the trees don't stand in full sun on the western or southwestern side of the garden - that's where the temperature swings are strongest.