Are social interactions always helpful in solving problems? Whenever there is a problem we socialize. When we are sick we go to a doctor. When we are hungry we go to a cook. When we want to laugh we go to a movie.

My question is : are these social interactions always helpful in solving our problems ? Is "if problem then socialize with right people" formula always helpful ?
Not always:

If you're sick and go to someone who's not a doctor, who's incompetent or a thief, that won't help (except perhaps as a placebo)
If you're sick with an incurable (untreatable) illness and go to a doctor, that won't help (well it might help with managing symptoms and explaining what's happening)

The Sigalovada Sutta (DN 31) details long lists of examples and differences, between &quot;good socialising&quot; and &quot;bad socialising&quot; for lay people.
I think Buddhism includes two themes:

Therefore, Ananda, be islands unto yourselves, refuges unto yourselves, seeking no external refuge; with the Dhamma as your island, the Dhamma as your refuge, seeking no other refuge.
Maha-parinibbana Sutta (DN 16)

and:

As he was sitting there, Ven. Ananda said to the Blessed One, &quot;This is half of the holy life, lord: admirable friendship, admirable companionship, admirable camaraderie.&quot;
&quot;Don't say that, Ananda. Don't say that. Admirable friendship, admirable companionship, admirable camaraderie is actually the whole of the holy life. When a monk has admirable people as friends, companions, &amp; comrades, he can be expected to develop &amp; pursue the noble eightfold path.
Upaddha Sutta (SN 45.2)