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To collect and re-check tour baggage you will not stay in the transit area and therefore will enter Thailand and are not eligible to transit without a visa. You should apply for a transit visa.
As per TIMATIC:
TWOV (Transit Without Visa): Passengers transiting through Bangkok (BKK) with a confirmed onward ticket for a flight to a third country within 12 hours. They must stay in the international transit area of the airport and have documents required for the next destination.
As you donβt stay in the transit area this doesnβt apply to you. You arenβt visa free to enter Thailand therefore you need a visa.
3 hours is a bit tight but the connection time should be fine.