I cut my calories, I'm working out and I am gaining weight. Why?

Firstly - MFP does not use the TDEE method to calculate your daily calorie goal. It uses the NEAT method. Familiarize yourself with how those both are calculated - just so you understand how MFP works so you can use it appropriately. You can absolutely use a TDEE calculator and manually put in your calorie goal though if you like.
I think that the TDEE estimate for you was likely... accurate if you are 'lightly active'.

So...if your TDEE starting point (bc it's still just an estimate) is ~2200....that is the amount of calories per day you could eat and theoretically stay the same weight. That is IF you are doing those activities consistently that you say.

So if you'd like to lose weight - you want to shoot to eat more than your BMR (~1600)...but less than your TDEE (~2200). So for you, you could manually set your daily calorie goal to ~17-1800 calories per day ---- do that for 4 WEEKS consistently --- accurate logging of food (if you use the TDEE method for calculating your daily calorie goal you should NOT track your workouts in MFP) and then weigh yourself and see what happened. Stay the same? If so, then you have better data about your actual* TDEE...great. Lost? Great, you are in a deficit. Gained, also great - bc again, now you know more information about your actual TDEE.

What you are currently doing - example: if you ate 1253 calories one day and burned 601 (if that's accurate as that seems very high to me...what workout and for how long was this?) --- then your NET calorie consumption for that day was only 652 calories - no wonder you felt lightheaded bc that's nothing. You are not eating enough. I know that sounds counterintuitive...but please trust me and eat the amount of calories you need to in order to do what you want to do. You are not going to even begin to get proper nutrition with so few calories. Also please note/remember that if you just started becoming more active than you've previously been --- your body will retain water weight. It has to - for muscle recovery...so that'll show up on the scale. It's not that you gained actual fat.

***You will not lose weight every time you weigh in. Water weight will be up/down. Things will go up/down based on how hard your workout was, what you ate, what part of your cycle you are in (if F)...etc. It's not linear.....that's why I *highly* suggest you do not weigh yourself every day --- and not even every week IMO. Every two weeks with the understanding that the weight will not go down EVERY time. OVER TIME is what you want to look at. My suggestion would be to get a bluetooth scale - they typically will give other stats (like body fat%, water, lean muscle, etc....) - I don't know how accurate that stuff is really but the weight is accurate and it can then track that weight into a visual graph on your phone and I found it exceedingly helpful to be able to see my trend line going down...even though every single time it didn't go down.

It's not just about cutting calories it's what you're actually eating and the timings. stop eating minimum 3 hours before bed. and the mistake is weighing yourself everyday, try minimizing it to weekly or biweekly and only when you first wake up. as for exercising, prioritizing it is important, walking on an incline for 30 minutes 5x a week should be great for weight loss...

good luck to us both