You're correct to tense abs during exercise. Doesn't sound like you have stomach fat getting in the way.
Here's my 0.02, take it or leave it:
Take a deep breath and check. Is your chest swelling or your belly? If chest, you're only using half your lung power. Practice getting breathing down into your belly. Get good, deep breaths down into your abdomen.
Next. Practice tensing your abs, then breathing deep into the belly. It might seem uncomfortable, as abs and lungs will seem to fight each other. Keep abs tight, maybe suck in a little. When your lungs inflate, it's like a big balloon in your torso. tightening abs and other core muscles will keep pressure on on that and make your torso really solid. It's vital for the big lifts. Practice taking a deep breath against hard abs, hold a split second, then exhale. If you feel dizzy, ease off a bit.
When you can do this readily, go to the weights. Take weight way, way down. Deadlift, for instance, should only be warmup weight or even lighter, like empty bar. Bend down and grab bar. Grip firmly, get tension on arms. Look straight ahead. Arch back. Now tense abs and get good deep breath. Yes, I know it feels weird, bending over, just do it. When lungs are full and torso solid, get hips down and lift. Exhale when you're standing up. Lower bar and inhale. Lungs should be full by the time the bar reaches the floor. Repeat.
Would be curious to know if this helps. If you're still having problems, you might want to check with a doctor or PT to see what's going on with your arms and chest.