Newbie needs help; am I doing this right?

Hello,
ok so I've been working out for 1.5 weeks now. I lift weights 4 days a week for 20-30 minutes (im usually sore the next day). I do 20-30 minutes of cardio 5 days a week. My weight is 160 and I am 5'5" and 24 years old. My bmr is about 1500. if Im sedentary it say I should be burning 1800. and if I factor in an activity factor of (1500 x 1.5) then I should be burning 2250 calories a day.

So should I eat my rmr of 1500 plus 300/workout day (assuming I burn 200 cals for a 30 minute cardio workout and 100 calories for a 30 minute weight training session)=1800 cals? Or am I supposed to add my workout calories to my sedentary BMR of 1800? I think that activity factor is overestimating the number of calories I burn. And the days I dont workout just 1500 calories because I heard the lowest I should go calorie wise is my rmr number.

In this last week and a half of working so hard I haven't lost any inches and I gained 3 lbs but I've been eating only 1200 calories so maybe im not eating enough but I don't really know how much I should be eating.Please help. This is so frustrating. Also, please give any suggestions as to what I should do?

I've always struggled with weight loss and always been a skinny fat 125-135lbs and have always eaten 1200 cals so I think my metabolism is shot. I had 2 babies in the last 3 years and I just want to lose weight the right way and be toned and thin this time around rather than skinny fat. Thank you in advance.