Brief Answer:
Paresthesias induced by medication Hydroxychloroquinine? YES

Detailed Answer:
The drug you have mentioned which goes by the trade name in the U.S. of PLAQUENIL clearly can cause side effects of PARESTHESIAS which are feelings of numbness and tingling which commonly affects fingers, hands, feet, toes, and sometimes parts of the face as well.

These effects are usually self limited which means that upon cessation of the medication the sensations will go away by themselves. There's no way to really accelerate the return to how you felt prior to taking the medication. However, in most cases, people are pretty much back to normal within several weeks. There are cases where the side effects can be much longer (months) and even more rare cases where they never go away. Let's hope that's not your case.

For your convenience I will include a list of the known side effects of this medication. I'm not sure why the doctor would not consider the medication as being the most likely reason for your symptoms unless he also has laboratory information that demonstrates a significant lack of certain elements in the bloodstream...but typically, if a patient has not paresthesias before administration of this medication and then, develops symptoms....we would simply discontinue the medication if possible and look for resolution of symptoms.

Here is the list of side effects for this drug:

Nausea, vomiting, Headache, Dizziness, Irritability, Muscle weakness, Aplastic anemia, Leukopenia, Thrombocytopenia, Corneal changes or deposits (visual disturbances, blurred vision, photophobia; reversible on discontinuance), Retinal damage with long-term use, Bleaching of hair, Alopecia, Pruritus, Skin and, musculoskeletal pigmentation changes, Weight loss, anorexia, Cardiomyopathy,(rare), Hemolysis (individuals with glucose-6-phosphate dehydrogenase (G-6-PD) deficiency), Prolongs QT interval, Ventricular arrhythmias and torsade de pointes
Vertigo, Tinnitus, Nystagmus, Nerve deafness, Deafness, Irreversible retinopathy with retinal pigmentation changes (bull’s eye appearance), Visual field defects (paracentral scotomas), Visual disturbances (visual acuity), Maculopathies, (macular degeneration), Decreased dark adaptation, Color vision abnormalities, Corneal changes (edema and opacities), Abdominal pain, Fatigue, Liver function, tests abnormal, Hepatic failure acute, Urticaria, Angioedema, Bronchospasm,
Decreased appetite, Hypoglycemia, Porphyria, Weight decreased, Sensorimotor disorder, Skeletal muscle myopathy or neuromyopathy, Headache, Dizziness,
Seizure, Ataxia, Extrapyramidal disorders such as dystonia, Dyskinesia, Tremor,
Rash, Pruritus, Pigmentation disorders in skin and mucous membranes, Hair color changes, Alopecia, Dermatitis bullous eruptions including erythema multiforme,
Stevens-Johnson syndrome, Toxic epidermal necrolysis, Drug reaction with eosinophilia and systemic symptoms (DRESS syndrome), Photosensitivity,
Dermatitis exfoliative, Acute generalized exanthematous pustulosis (AGEP); AGEP has to be distinguished from psoriasis; hydroxychloroquine may precipitate attacks of psoriasis, Pyrexia, Hyperleukocytosis

Your problem of numbness and tingling in the above list goes by the technical name of SENSORIMOTOR DISORDER which is another way of saying either NEUROPATHY or PARESTHESIAS.

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This query has utilized a total of 48 minutes of professional time in research, review, and synthesis for the purpose of formulating a return statement.

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