Can high stress and anxsity cause symptoms that aren't really there?

Yes.: It is call Psychosomatic symptoms like headache, Nausea, etc. Therefore try to develop relaxation technique, meditate, exercise regularly and take one thing at a time

Most certainly: Anxiety and "stress" commonly manifests as physical symptoms. Common complaints related to anxiety are nausea, palpitations, abdominal pain, sweating, shortness of breath and a host of others. Your mind is exceedingly powerful!