It takes a LOT - a real lot - for women to bulk up: I can deadlift 1.5 times my bodyweight and I still wear size 10 trousers & have a flat bum. Get that fear out of your head.
The DOMS you describe is just discomfort from cross-training, but you might also not be doing appropriate mobility & stretching. The DOMS will go away as you start to move in your walk/jog/run, and your body will adjust.
But in terns of strength training, you are doing too much in one session, and not heavy enough. It is better to do fewer reps, but heavier, and try to strength train twice a week, so you can break down this one huge session with 2 rather more focussed ones.
My routine is:
Leg raises x 34
Bench chest press with 7.5kg dumbells x 36
Situp using 5kg weight on chest x 30
Calf raises with 20k bar on back x 45
30kg deadlifts x 36
30kg squats x 36
Abduction/adduction 27kg x 42 for both
Assisted pullups x 36
And to be honest, I don't see the logic of this programme. If you do squats with a heavy enough weight (counting the bar @20 kilos - try for 45, so try putting a 10k plate on each side, and work up) you could do 3 sets of 5 reps, with a 2 minute rest in between. The last rep of each set should be only just manageable - you should be a bit puffed out by the end of a set.
I only do 12 reps of squats in a set as a warm up, and I just squat the bar (20 k).
Why leg raises, calf raises, squats and abd/adduction all in one session? Choose 1 main lift - the squat - and go heavy. Then maybe a couple of accessories that you do unweighted, such as lunges and step ups (onto a box) or even box jumps (jumping up onto a plyo box), which help with mobility and bounce.
Then do deadlifts for your whole posterior chain (back, glutes, hammies) plus maybe something that focuses on back mobility & flexibility - Jefferson curls maybe? (very carefully at first).
Then a cool down which focuses on flexibility & mobility in your hips, quads, ankles, and calves.
How is your flexibility generally? can you do the shin box move for your hips? Can you get your fingers to your toes? Can you swing your torso to the side, keeping your hips facing forwards?