Why are nausea and dizziness such common side effects from medication?
Some medications because they are taken orally do cause nausea. Many medications, because they have an effect on blood pressure, or are central acting in some way, do cause dizziness. However, nausea and dizziness in particular are two highly subjective symptoms which are difficult to quantitate or verify, and which can occur with simple anxiety or stress. Several more such highly subjective and difficult-to-verify symptoms are numbness, tingling, headache, insomnia, fatigue and difficulty concentrating, all of which can be brought on by stress.

Switching for a moment to a drug with a measurable side effect of beta-blockers: erectile dysfunction (ED). In a study of men treated with beta blockers, the patients were separated into three groups with the following results:
a) the group who were not told the name of the medicine nor informed of the ED side effect had the lowest incidence of ED (3.1%)
b) the group who were told the name of the medicine but not informed about the ED side effect had a 15.6% incidence of ED
c) the group who were told the name of the medicine and informed of the ED side effect had the highest incidence of ED (31.2%)

Hypervigilance is an increase in attention to bodily cues or symptoms for any reason. It has been well documented in many studies that if you give one group of people a list of possible negative side effects, and another group a list of possible beneficial effects, then give both groups placebos (usually a small coated sugar or cornstarch tablet), the first group will experience negative effects while the second will feel better. The negative expectation producing a negative side effect is called the nocebo effect (the opposite of the placebo effect). 

Interestingly, recent studies where anti-anxiety medications were administered before the nocebo dramatically decreased the nocebo effect.

For ethical reasons, in all clinical trials of drugs, patients in the treatment group and the placebo group must be given an extensive list (standardized) of possible negative side effects, introducing a negative expectation into both populations.

Two of the most common negative side effects in both groups are dizziness and nausea. Therefore, they must be reported as possibly occurring side effects with the medication.

This is not to say we're all imagining things. Nocebo effects have been correllated with reproducible effects on functional MRIs. They have a basis in reality, even if it's caused by negative expectations.

It's a problem being discussed a lot now by medical ethicists.

The influence of the nocebo effect in clinical trials
Avoiding Nocebo Effects to Optimize Treatment Outcome