This is what everyone seem to experience when first starting out on spinning so stay cool https://www.studioveena.com/img/smilies/icon_cool.gif.
I remember when this question was up like half a year ago. We suggested to the thread starter that she'd film herself and then, when she watched it, she realized that she actually didn't spin at all as fast as she thought she had done. It may FEEL really fast though as you are perhaps not used to all the spinning forces. It doesn't take too much for them to act strongly on your body.
You are doing right not sweeping your leg in the fireman, as that will set off the spin a lot. It may take some time, but you'll learn how to handle it and how to give the pole the amount of momentum that you want. There's a reason why most studios teach new students on static first. It's more difficult on spinning and takes more strength for example.
I understand that the climbing feels hard for you. You'll have to learn doing it carefully so that you're not giving the pole an unnecessary push when you mount it. I find that it's easier to control the speed by placing the sole of my left foot (when spinning clockwise) on the pole first, before I grip the pole with both legs, keeping the free leg stretched out and close to the floor.
I guess the explanation in words didn't make too much sense https://www.studioveena.com/img/smilies/icon_e_wink.gif so I will give you a link where you'll be able to see what I mean. I'm not done editing this video yet though, but hopefully tonight! I'll post here then.