MySQL Performances Issues
In your question, there is not enough information to see where the problem is from technical point of view; however, I can see that there is a problem in communication between you as developer and the DBA. This is not abnormal though as DBAs and devs do not always 'speak the same language'.

Let's go the some points in your question:


You should rely on the 'slow query log' to get your slow queries. Monitoring them in PHP may not be accurate measurement for slowness of the queries.
The query that took very little time in PhpMyAdmin could be cached. Use "SELECT SQL_NO_CACHE", and repeat at times that are not close to each other to avoid hardware level caching.
"SELECT *" vs "SELECT field1, field2": If you don't need all fields in your result, don't use "SELECT *", as it will waste resources sending non-wanted values. 
"Too Many Connections" could be of different reasons, one of them is slow queries that lock the tables so other connections are waiting and piled up to the max where the server refuses new connections. 


My recommendation is that you talk to your admin and work both as one team, not as two separate teams. 

HTH