It’s interesting your doctor prescribed Zetia (Ezetimibe) only. It’s normally used in conjunction with a statin for people who can’t achieve goal on a statin alone. On average, Zetia is about 1/3 the potency of most statins.

Yes, there can be potential Zetia related side-effects, but they are uncommon. The following is on the Mayo website https://www.mayoclinic.org/drugs-supplements/ezetimibe-oral-route/side-effects/drg-20067172.

Less common:
Body aches or pain
chills
cough
diarrhea
ear congestion
fever
general feeling of discomfort or illness
headache
loss of appetite
loss of voice
muscle aches and pains
nausea
shivering
sneezing
sore throat
stuffy or runny nose
sweating
trouble sleeping
unusual tiredness or weakness
vomiting

Incidence not known:
Black, tarry stools
bleeding gums
bloating
blood in the urine or stools
burning, crawling, itching, numbness, prickling, "pins and needles", or tingling feelings
chest tightness
constipation
darkened urine
difficulty swallowing
discouragement
fast heartbeat
feeling sad or empty
gaseous stomach pain
hives, itching, skin rash
indigestion
irritability
large, hive-like swelling on face, eyelids, lips, tongue, throat, hands, legs, feet, or sex organs
light-colored stools
loss of interest or pleasure
muscle cramps, pain, spasms, stiffness, tenderness, wasting, or weakness
pains in stomach, side, or abdomen, possibly radiating to the back
pinpoint red spots on the skin
puffiness or swelling of the eyelids or around the eyes, face, lips, or tongue
stomach pain
trouble concentrating
unusual bleeding or bruising
yellow eyes or skin

Some side effects may occur that usually do not need medical attention. These side effects may go away during treatment as your body adjusts to the medicine. Also, your health care professional may be able to tell you about ways to prevent or reduce some of these side effects. Check with your health care professional if any of the following side effects continue or are bothersome or if you have any questions about them:

Less common:
Back pain
difficulty in moving
joint pain
pain in the arms or legs
pain or tenderness around the eyes and cheekbones

Other side effects not listed may also occur in some patients. If you notice any other effects, check with your healthcare professional.