It is more than likely either an exhaust leak or a valvetrain issue.
But honestly, the only real way to find out is to either take an automotive stethoscope and listen to the engine at every area around both valve covers and the exhaust manifolds and head pipes, and/or do some teardown to see if their is any visible wear or damage.
The mechanic that told you to drive it till it breaks knows that something relatively minor is wrong now, but will blow up into a much bigger problem in the near future that would more than likely end up with you replacing the engine, I wouldn't be taking it back to him.
There are a couple of "mechanic in a bottle" remedies you can try to see if they help things any:
Lucas Oil Stabilizer will thicken your oil and cushion worn parts. This will help prolong the life of the engine with it's current problem (provided it's worn valvetrain) but it will not fix it. I use it in all my older vehicles to help keep oil pressure up due to wear on the bearings, just use it in place of a quart of oil at your next oil change.
Marvel Mystery Oil will clean out any debris in the valvetrain and free up sticking lifters. If replacing a quart of oil with this gets rid of the noise, then you may not need to visit a mechanic after all, just use this in place of a quart of oil at your next oil change and drain it out with the oil in 3,000 miles.
Seafoam or B12 Chemtool will also clean your engine, and do it much more quickly, you add either to the oil right before you change it, run the engine a few minutes, and then drain the engine and fill with fresh oil. Both work extremely well at cleaning things out.
The only problem with trying any of those is that they could just "mask" your current issue (Lucas) or even make your current issue worse (Marvel, B12, Seafoam) the issues you could be having in the valvetrain could be a bent pushrod, a loose rocker arm, a collapsed lifter, a sticking lifter, a lifter that's roller bearings have seized, a bent valvestem... it could be several things. A collapsed or sticking lifter can, in many cases be cleaned by the cleaning additives listed above, but it is something that will recur and need to be treated regularly unless you actually go inside the engine and clean or replace that lifter. Any of the other situations will only get worse and intensify until something finally does break.