My mother swum in our pool while we were away and it was going green with algae. she said she didn't go under though. can she get sick?

Sounds ok: Unless she ingested some of this "eeky" water with algae, she should be ok. I have no idea what else you had/have in that pool. It's not likely that there are some tropical water-born parasites or other organisms that could cause concern. Does she have any open wounds? Did she aspirate any of this water? If the answer is no to most of these questions, she should be ok. No fever, or GI upset?