Thank you for the added information.
It is impossible ,in my opinion, to perform a dental extraction
,without any kind of sedation.
It is quite possible that you are allergic to certain medications.
However,there are various types of anaesthetic agents that are being used and it is likely that you are not allergic to all of them.
You would have to find out which drugs /medications you are allergic to.You can visit your doctor ,who could help you in finding this .An Allergist would be able to help you.
You can also consider getting dental treatment performed in a hospital that provides emergency medical treatment,in case there is an allergic reaction.
You can also consider visiting an Oral Surgeon.An experienced Oral surgeon can perform these extractions ,in a hospital setup.
Alternatively ,you can consider visiting a dental University,where a comprehensive dental treatment can be performed.A Dental University Would have an in house doctor,anaesthetist and dentist always available and a co-ordinated treatment can thus be performed.
You can visit an Allergist to find out which drugs and medications you need to avoid.