@annmarkerls I have a few things to hit on this
First: push ups are hard. In general it's a better idea to go with an easier variation (such as incline pushups) with full sets/reps with good form instead of throwing yourself at a variation that is too difficult for your current strength level. Try doing 3 sets of 8-12 pushups at like, kitchen counter height, and if you can do that with good form then try dropping down to weight bench height for your pushup sets
Secondly, if you're comparing 1 pound of muscle to 1 pound of fat? The muscle takes up way less space than the fat despite the weight being the same. Weight isn't a great heuristic, but it's easy to measure so people use it. I wouldn't bother weighing yourself more than once a week since basic things like when you last ate, drank water, or used the restroom can make your weight fluctuate 2-5 lbs easy, and since you're female any hormone cycle related fluctuations can also impact it via water retention
Thirdly, recheck your TDEE figures. The light exercise TDEE for your height/weight/gender is likely ~2,000 so you likely need to be targeting around 1,500-1,800 kcal a day (again on average, your body doesn't care if some days you're slightly over/under that target)
You didn't mention how long you've been working out, but it can definitely take 2-3 months or so to start seeing visible results when you start working out more seriously. I wouldn't focus on the scale, I would focus on how you feel and how your clothes fit since the same weight with a lower body fat percentage is a win