Why Am I Gaining Weight on this Meal Plan? I want to maintain.

Have you set MFP up for maintenance? is 1700 what it gave you?

Weight gain when you up your calories is very common, as you're replenishing glycogen stores which will cause additional water weight. With your stats and history I wouldn't drop your calories at all.

Unless you are extremely small-boned (like some Asian women are), your ideal weight is probably closer to 120-125. A basic formula is 100 lbs for 5 feet, and then 5 lbs per inch (for women; for men, it's 7 lbs per inch) over 5 feet. When I check those weights in a BMI calculator for people of different heights, the formula weight usually ends up right smack in the middle of the normal/health range--equal distance from underweight/overweight. So, perhaps you are gaining precisely b/c your body needs a few extra lbs. If you don't like the way it looks, change that weight from fat to muscle-recompositioning, as it is called here.

The number on the scale is only 1 measure of fitness--and you are wise to notice that eating too few calories affects your mood and energy. Don't let some arbitrary number get in the way of good health. Try to figure out a way to make some time for exercise (google "strength training throughout the day") and focus on over-all health, not just the scale. Good luck, whatever you decide to do.

Meal plan is irrelevant.
Calories are what count here.
If you are gaining then that means you are eating above your maintenance.

Your weight will go up and down for a lot of reasons that have nothing to do with fat gain. Mainly, these are fluctuations in water weight. Water weight fluctuations are part of how a healthy body operates. Since they aren't fat gains, there's no need to worry about them.

Some possible reasons one's body may temporarily retain extra water: Healing from an injury or surgery, repairing muscles after a new workout, a minor disease or infection that involves inflammation, extra sodium or carbs eaten (more than normal, even if a perfectly healthy amount of either or both), various stages of a pre-menopausal woman's menstrual cycle. (I'm sure I've forgotten some.)

Yes, for someone your size, 5 pounds is a possible water-weight fluctuation. Some women routinely gain and lose that much or even more over the course of a menstrual cycle. Other things on the list of potential causes can add up to 5 pounds, too. If you didn't eat 17500 calories more than your maintenance - and I'll bet you didn't - you didn't gain 5 pounds of fat.

It's correct as stated above that when you go to maintenance, glycogen replenishment (perfectly normal and healthy) can cause a little water weight gain. It isn't fat. Also, if you start eating 500 more calories of food every day, the average in-transit contents of your digestive system are simply going to weigh more, and that will show up on the scale. It isn't fat, either.

If MFP says you should eat 1800 to maintain, eat 1800. Eat that for 6 weeks, and see how your weight behaves over that time period. (At about your height and weight, I maintain at a calories above that, and I'm over 60 years old). Even if it's an over-estimate, you can only gain a tiny, tiny amount. The 1800 is more likely to be accurate, or even under-stated, but you'll never figure that out unless you eat at that level through a whole menstrual cycle plus a couple of weeks, and see how things average out over time.

If this is freaking you out, one option would be to start at a calorie level where you've been losing weight, then add 100 daily calories every day, jumping that much up once every week or two, until your weight stays more-or-less stable for a full month (there will still be water weight fluctuations!). This gradual add-back strategy, though, will tend to hide any glycogen replenishment & higher average digestive contents in a very slow rate of continuing fat loss, so there's less drama on the scales because of that. Some people also find that a gradual add strategy helps them become gradually more energetic in daily life, and restore some of the calorie burn lost to adaptive thermogenesis (the thing people call "metabolic damage" that isn't really metabolic damage), if there was some.

Best wishes!