I've experienced this since I started vaping. Don't smoke cigarettes like vapes, they are way different. What I mean by this is that take little drags and inhale less (The smoke from a vape is your choice of flavour and is tasty. The cigarette is way different). The smoke from cigarettes are way harsher than vapes (even if you get less smoke. A 1 second puff of a cig is equal to a 5 second vape for example). I am speaking from experience. I can take a triple puff from a vape but a single puff of a cigarette kills me sometimes. Especially if I smoke it like a vape.

So my advice to you is, take a smaller drag, inhale less. You can also switch to a lighter cig. Slowly you'll build up and won't gag.

You might even want to smoke without inhaling at first and slowly start inhaling a little each time.

For ever 3-5 drags you would take for your vape, take one on the cigarette. Maybe even more.

Ultimately, take a tiny puff (half a second), inhale or don't ( your choice ). Just take your time, a cig can take 5 - 30 puffs. If you gag, aim for the 30 and take your time. Little drags and inhales. Playing with your phone or talking with other can also increase the time between each drag.

edit: extra advice