Gaining weight

essentially yes, at the very least you need to eat at your BMR, to get the best results you need to figure out your TDEE and eat that at a small deficit, 15-20% less

1. You ate something high in sodium within a couple of days of the weigh-in.
2. You have not pooped recently or you ate more (by weight, not calories) than usual before your weigh-in.
3. You are not used to so much physical activity, so your muscles are hoarding water.

Four days is really too soon to have an accurate sense of whether MFP is giving you a good target. Body weight can easily fluctuate by five pounds in either direction on any given day, whereas most people should only be losing up to 2 lbs a week. Keep eating at your goal (the original one) for a month and see what happens.

DOMS = delayed onset muscle soreness and does not cause weight gain. However, weight lifting/sudden increase in exercise after a long period will cause your muscles to swell and retain water (with or without DOMS) which can cause weight gain.

It's only week 1, i wouldn't even bother looking at the scales for another few weeks, you need to understand that scales are not the be all and end all of success/progress.

Just have a look in the mirror or start checking your body part measurements or if you don't want to do that then simply just keep an eye on your clothe sizes

You will start to notice a difference in time, don't fret

there are a lot of things that could make your weight fluctuate that rapidly in four days.

-you could be weighing yourself incorrectly. make sure you are weighing yourself at the same time in the same situation (the best way to do it is to pick a single day out of the week, i picked monday, and weigh yourself in the morning right after you wake up before you eat or drink anything, and you should not be wearing any clothing). The reason you want to do this is because your body fluctuates in weight during the day so stepping on the scale at different times can show you different weights. Sometimes my weight fluctuates as much as 3-5 pounds just from drinking water and not yet peeing.

-water weight. This is probably self explanatory. your body could be clinging to water for different reasons (high sodium in your diet, high carbohydrates, or you could have weighed yourself after drinking a lot of water).

there are others also but you get the point. just stick with what your diet is telling you, stay away from the scale until next week, and then in a few weeks i'm sure you will see a drop in weight as you expected (as long as you aren't overestimating exercise calories and underestimating your caloric intake, which alone or combined can destroy any calorie deficit you think you might have. measure everything you eat and don't go overboard with tracking your exercise calories.

sometimes when you start a new exercise program your body will retain fluid, making it appear as if you gained weight.

In all reality you have not gained weight, it is just the body holding on to fluid to cushion your muscles and try to repair damage or unaccustomed strain.

drink your water, avoid salt like it carries bubonic plague.

give it 2 weeks, I promise it will get better. Hang tough. Although do make sure you are eating enough food, set your goal weight loss lower and take it slower, you will be more grateful for it in the long run. I learned that the hard way.

it's normal, relax and don't worry.

Give it more than four days, too. Depending on how drastic a change this has been, your body is likely still adapting. Your body's not like a bank account where it instantaneously gets smaller the moment you spend more than you take in.

Edit: Dangit. That's what I get for pausing to have a conversation in mid-post. I end up finding out too late that people have already made the same basic comment while I was distracted.

not being smart here, but give it more than 4 days.

Bingo!! We have a winner!!