The verb suggest cannot be followed by object + infinitive. That-clauses and –ing forms are common.

Father suggested consulting a doctor. OR Father suggested that I should consult a doctor. (NOT Father suggested to consult a doctor.) (NOT Father suggested me to consult a doctor.)

Verb forms in that-clauses after suggest

In that-clauses after suggest, various verb forms are possible.

In British English, should + infinitive is common.

She suggested that I should get a job.
She suggests that I should get a job.

In American English, should + infinitive is rare. Instead Americans use a special verb form called subjunctive.

She suggested that I get a good job.
She suggests that I get a good job.
I suggested that he hire an attorney.
I suggest that he hire an attorney.

In British English, ordinary present and past tense forms are also possible.

She suggested that I got a degree in physics.
She suggests that I get a degree in physics.
I suggested that he consulted an attorney.
I suggest that he consults an attorney.

Suggest can be followed by a direct object.

What shall we eat? I suggest fish.

Suggest cannot be followed by an indirect object without a preposition.

Can you suggest a nice restaurant to me? (NOT Can you suggest me a nice restaurant?)