Always try simplest/cheapest options first before jumping the gun.
When engine is cold remove radiator cap make sure coolant is full and start engine and let idle for a few minutes (only).
Do you see a constant stream of air bubbles appearing in the coolant?
If answer is no:
Remove radiator and take to repairer and ask for flush and reverse flush and pressure test and repair if necessary.
Reinstall and run engine without radiator cap (as above).
Let us know results and if there is any change.