When engine is started the vehicle shakes , sounds good but the engine isn't cammed so it isn't supposed to sound like that

I have a vibration starting around 35 and increases with speed. Not a wheel balance or uneven wear vibration. This is a heavy vibration that shakes the whole truck but not the steering wheel. Thinking maybe a broken belt in the rear tire or drive shaft related. Does have a/t tires installed but no uneven wear. Tpms sensors not reading on both right side wheels makes me believe they might have hit something and damaged a wheel/tire but no visual evidence found. Does not increase with rpm or reduce when coasting. Ive inspected everything visually and all looks good but next step will be to get it rolling in the air to see if anything is out of balance or loose.

I was driving it and then I heard a slight thud and then it started to tick and whenever I had it parked I was getting shaken inside the cab like it had bad hypothermia, im unsure what it is.

The truck doesn't have 100% power and is shake a lot when you drive