When the problem began it was only loud when the fan first kicked in and made almost a clanking noise like something may have been loose. Now it is always loud and running really fast. It almost sounds like an old window fan on high with something to close to the front of it.

Well it would help to know which fan is making the noise. Most heat and air systems have at least 2 fans and sometimes 3. 1 outside in the condenser unit and 1 or 2 more in the furnace.
Sounds like a possible damaged or loose fan blade wherever it is.. whichever it is you shouldn`t run it till it has been checked out, it could cause even more and expensive damage

It is inside the furnace.

It sounds like it may be in the blower motor, that is also the only place I see actual fan blades.

With the power off,, reach in and turn the fan manually is it rubbing or hitting anything? Making a rattling noise of any kind?