My husqvarna chain saw model 345 acts as if the brake is on but isn't. It will start the chain moving if I hold down on the throttle but it starts quick and acts as if it is heating up.

Without the chain, will the saw start and rev? If so, you may have the wrong chain (gauge) and bar.

gas bleeding off the carb someplace

I'm guessing from the statement that it "will not work to increase speed" that you have been able to successfully start the chainsaw.
I have to look at this with the assumption that you haven't run a chain saw before, so bear with me if some of this is excessively simple.
If the throttle trigger does not move, something is jammed. The handle for the choke should automatically move to the retracted position when you pull on the throttle. If it doesn't, see if the trigger will move after you push the choke handle back in.
If the trigger moves in when you squeeze it but you don't hear any change in the engine sound then it's probable that the throttle wire has disconnected at the carburetor or at the handle.
Is the chain brake off? You need to pull it firmly back toward the upper handle for it to be disengaged. If the handle is forward it will lock the outer portion of the clutch. If you try to accelerate with it locked the engine will bog and not allow the chain to move.
Any of these conditions other than the chain brake will probably require some disassembly. Make sure you're confident that you've correctly reassembled everything if you're going to do it yourself.

Not all 345 machines had an adjustable oiler, it is retro fittable if it does not, however if it hs an adjuster, the screw is located on the bottom of the saw between the cranckcase and the fuel tank, just below the sprocket, there will be an oil symbol and a - and + sign there, the pump is three position, for 13/15/18" bars.

Check for wear on the plastic end of the throttle push rod, if so it tends to catch where it comes out of the fuel tank, replace if worn.

Turn the Hus 345 chain saw upside down, you may see a little Icon of a oil droplet and a + - arrow by the chain. THe adjustment screw is not pictured in any of the standard user manuals,. but it is a small black slot headed screw over a rectangale metal tab by the chain. I believe if you turn it counter-clockwise, it will give you more oil,, It did for me. If you have the bar off, you can start the saw and see it come out the hole, that would verify your oil pump is working. Make sure the holes on the bar are clean also. running the saw at a fast idle for 1 min should oil the chain well enouth that it starts spraying off the end of the bar when you gun the engine.

has the chain ever came off the saw?and i'm going to assume that it is the correct chain for the saw...reason i ask about the chain comming off the saw is that when it does the driver have a tendency to become nicked and will heat up the clutch because the saw is trying to drive the chain links through the chain slot.also you need to look at the drive sprocket to see if there is any wear on the teeth....also over tighting the chain will cause the clutch to heat up.

Replace the bar. Your bar has gone bad and that is why you are losing power. Bars are made by the chain saws to be completely oiled at all times. When the bar does not get oil the bar will start to warp and that is what will cause you lack of power when trying to due a top cut

If it idles it is not flooding out as it it most vulnerable to flooding at idle if the stalling is happening as you try to throttle it up it is likely starved for fuel. Start by changing the in tank fuel filter, and the spark plug. good chance that will solve your problem. If it does not Turn the high idle screw out in 1/8 turn increments try running the saw after each adjustment. Keep track of the amount that you turn the screw. you might have to put it back to its original position. Some times adjustment screws will vi berate out of adjustment and other times crud will cause fuel restriction opening the screw allows for a larger port for any restrictions to pass through. After you use the saw for a short time turn screw back in if it starts to stall at idle or you notice increased smoke.

adjust the gas by turning the screw on the carburator