Perfectly normal reaction the first time you do any new scary thing.
For most people, the nausia disappears after a few more jumps.
Altitude sickness ... errrr ... low oxygen density is rarely a problem during skydiving because few jump planes climb more 14,000 feet above sea level. For comparison, airline cabins are pressurized to 5,000 maybe 8,000 feet ASL, but much of that is to accommodate grandmothers with weak lungs. Time also affects hypoxia (shortage of oxygen), but jump-planes rarely fly more than 5 minutes above 10,000 feet, so that is not an issue for people with healthy lungs.
Yes, clearing your ears (Valsalva Maneuver) can reduce sinus pressure, reducing the risk of head aches, nausea, etc. I usually clear my ears two or three times on the way up and once after opening.
Low blood sugar can cause nausea ... even fainting ... after opening. We did not understand this until we had been doing tandems for a few years. Basically, any scary sensation causes your body to produce huge amounts of adrenaline and burn through blood sugars at a rapid rate. Once the skydive slows down ... after opening ... you relax, maybe even pass out. The cure is nibbling on snacks and sipping water all day.
Also consider that fear levels drop by half during every one of your first few jumps. Fear will never go away, but the curve will flatten out in a logarithmic way. If you get too relaxed, and no longer fear skydiving, then you should quit, because you have lost track of how dangerous the sport really is. Smart skydivers are always a little afraid, but learn how to channel that fear into equipment checks, pre-planning, altitude checks, etc.
Older (pre-2000) tandem harnesses were more likely to put too much pressure on your stomach. Modern tandem student harnesses have lower belly bands, so are less likely to cause nausea. If you feel nauseous under a tandem, simply ask your instructor to loosen the belly band a bit after opening.
Many tandem students complain about leg straps being too tight, but fail to realize that all their weight is resting on those leg straps. Tough!
OTOH loose leg straps can bruise during opening shock, so better for your instructor to tighten leg straps a bit too much ... rather than lose you at opening time.