The symptoms you describe are non-specific and can be due to a variety of causes.
I agree with the rheumatology evaluation. This should include an ANA level and rheumatoid factor.
Regarding the dizziness, a referral to a neurologist and appropriate brain imaging should be done to evaluate for masses or other neurological diseases.
The swelling may be due to cardiac, vascular, or kidney diseases. Blood tests to evaluate for kidney function as well as an echocardiogram to evaluate the heart can be considered.
As for the alopecia and the skin lesions, appropriate biopsy of the lesions can be considered. A referral to a dermatologist can be considered to explore this avenue.
These options can be discussed with your personal physician.
Followup with your personal physician is essential.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
Kevin, M.D.
kevinmd_