Gingivitis is anytime your gums bleed. It's a scientific term for inflammed gingiva (gums).
If you had a thorough check-up they would have done what's called a periodontal chart. That is where they basically measure how deep the space is that they are cleaning out. 1-3mm is healthy. 4mm are so-so and 5mm and above are not good.
5mm pockets can mean your gums are super swollen or there is bone loss. Bone loss is periodontal disease. This is what you need to find out if you have and to what degree. Bone loss is not reversible like gingivitis is. It doesn't sound to me your dentist checked this and took the time to explain gum diseases to you. You seem genuinely concerned about your dental health. Next time - ask more questions - it's easier to help you when we can actually SEE whats going on as well
As for now, keep up with the flossing. There is no way to say for sure how long it will take for he gum inflammation to go away completely but 3 spots isn't terrible. Also you may want to invest in a sonicare toothbrush. They are GREAT for puffy gums bc they vibrate and its like massaging your gums while cleaning your teeth. I always compare it to walking without shoes on - your feet would get touch but its a good thing to have tough gums! They are pricey but a great investment - it's all I use!
I am a dental hygienist. Have been in dentistry for 14 years. If your dentist cleaned your teeth - request a hygienist next time! Or find a dentist who has a hygienist on staff. Most dentists i know of that have cleaned teeth, don't do it as well as they should mainly because its not as important to them as fillings, root canals, caps etc. They don't get much time in school for hygiene and they didn't become dentists to clean teeth really...and I can't say I blame them lol!