Should I test for what kind of food my new born baby allergic to before offering solid food?

Generally unnecessry. Food reactions in infants can vary from simple spitups to recurrent vomiting, loose stool to copious diarrhea, nasal congestion, hives etc. Simply delaying foods until the baby sits up can avoid the impact of a food reaction as a bigger baby can handle it. A calander of what u add/when & what events happen over several days is adequate to monitor rxns. Testing should be limited to confirming allergy.
No solids yet. You should not offer your newborn solid foods or anything other than breast milk. As your baby grows, there is a generally accepted calendar or schedule you can follow so that you don't provide the wrong kinds of foods too early to your toddler.