More than 50 people are being treated at the hospital in the town, which is on the shores of Lake Chad.
The camp on the town's outskirts is home to tens of thousands of Nigerians who have fled Boko Haram attacks.
Chad is host to a new regional force set up to tackle the Nigeria-based militant Islamists.
Benin, Cameroon, Chad, Niger and Nigeria agreed to establish the 8,700-strong force, but it has yet to start operations in earnest because of reported funding difficulties.
At least 37 people died in the Baga Sola explosions on Saturday afternoon.
This figure may include the suicide attackers, which some reports put at five.
Witnesses reported hearing three blasts, one at the busy fish market and two at the refugee camp.
Officials suspect Boko Haram to be behind the attacks - the group first attacked Chad in June using suicide bombers to target the capital, N'Djamena.
Since then Chad has banned people from wearing the full-face veil, fearing attackers use the garment to cover explosives, and reintroduced the death penalty for acts of terrorism.
Borno state, which has been at the heart of Boko Haram's six-year insurgency, is on the Nigerian border with Chad.
Earlier this year, Chad was instrumental in helping Nigeria's army retake most of the areas Boko Haram occupied.
But in the last few months, suicide attacks in particular have intensified.
This week, two new Boko Haram propaganda videos have been released with footage suggesting it still has scores of fighters.
In one of the videos, the group reaffirmed its allegiance to the Islamic State group and its leader Abu Bakr al-Baghdadi.
According to Amnesty International, at least 17,000 people, mostly civilians, have been killed since 2009, when the group launched its violent uprising to try to impose militant Islamist rule.
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Suicide bombers have attacked a fish market and refugee camp in the town of Baga Sola in western Chad, killing more than 30 people, officials say.