Long post alert:
I'm convinced your bad experience was down to three factors; going ATG, poor, bubbly, wet lather, and blade angle and/or pressure.
For what it's worth (I've been DE shaving for about 14 months), I think you need to think about a few technique modifications. I don't claim to be an expert, but I found these areas very important when I took up DE shaving. Firstly, you need to check the mantic59 Youtube videos, especially those on lathering. A good cream, such as Palmolive (my favourite budget cream) is easy to lather with a half-decent brush as long a you do it correctly. Squeeze more water out of the brush and swirl for about 30 seconds, which should give you a thick, dry "proto-lather". Then, drip a few drops of water from your fingertips into the bowl and swirl for another 30 seconds. Repeat a couple of times and you'll see the lather build, become glossy and all visible bubbles disappear. Pull the brush vertically out of the bowl and you should see a peak of lather on the end of the hairs of the brush. Gently shake the brush, bristles up, and watch the peak If it collapses, the lather is too wet and/or needs more mixing. If it's short and doesn't move, it's a touch too dry - add a 2 or 3 more drips of water and keep mixing. What you want is a peak that wobbles slightly, that curves at the end, but doesn't collapse. Then, take some of the lather between your thumb and forefinger, and rub them together. The lather should feel slippery and protective, and should prevent you from feeling the texture of your fingerprints. Do this a few times without shaving - Palmolive is cheap and it's no waste if you're learning. Get used to the way the lather builds and changes as more water is added.
Once you've got the lather sorted, your next consideration is preparing the beard growth. Either shave just after a hot shower, or soak a flannel in hot water (properly hot, not merely warm), squeeze the excess out and hold it against your face and neck for at least two minutes, re-wetting it as it cools. I can soon tell when I've not properly prepped my face as I get the same tugging sensation you mentioned.
Next (and last) is using the razor properly. Don't grip it with too many fingers, and don't hold it up near the head end. Place your little finger under the end of the handle and support the handle between your thumb and first two fingers. Don't grip is, cradle it. Rest your ring finger on the handle if you want but don't use it to actually hold the razor. To get the right blade angle, hold the razor against your cheek with the handle horizontal (parallel with the floor). Very slowly slide it down your face whilst lowering the end of the handle. As soon as you feel the blade touch your skin, stop, and look at the angle of the razor in the mirror. Try to replicate that angle when you shave. Finally, (and this will be easier if you hold the razor as I described), don't apply any pressure from your hand through the razor. Literally just let it rest on your face with the weight of the razor head. Get used to how that feels so that you can replicate that under the chin when gravity is tending to force the razor away from your face; in that case, you do have to apply a tiny bit of pressure to maintain contact between blade and face, but no more than you felt as you rested it on your face.
Good luck, and sorry for the long post, but these things aren't easy to explain.
