1. It was way too early to put an anemone in a 2 month old tank.
2. All algae is caused by two major things: lights and nutrients. Limit light or limit nutrients and it will go away.
Here's a link to a few articles that deal with reducing nitrate and phosphate, tank maintenance, and good husbandry skills.
https://forums.saltwaterfish.com/t/388776/snakes-methods
Especially these links:
https://forums.saltwaterfish.com/t/388803/snakes-methods-for-basic-husbandry
https://forums.saltwaterfish.com/t/388800/snakes-method-for-hair-algae-removal
https://forums.saltwaterfish.com/t/388923/snakes-methods-for-reducing-nitrates-and-phosphates#post_3433119
https://forums.saltwaterfish.com/t/389167/snakes-method-for-water-quality-troubleshooting#post_3437299
https://forums.saltwaterfish.com/t/388805/snakes-methods-for-water-changes
Anemones have a 90% chance of dying in the first year. If your tank is less than a year old, it's more like 95%. I wish you the best of luck, and if any of those articles can not answer your questions, please feel free to private message me.