Two professors declined to write LOR for me because they are busy?
There's a chance they're trying to avoid writing the LOR because they don't think they can write one that's good enough to help you.

If an instructor can't write an LOR they think will actually help a student based on what they know to be the truth (even if only because they don't think they know you well enough), most instructors will try to encourage the student to go to someone else.  No one likes writing a bad reference.  But they also struggle with how to do that without hurting the student's feelings.  Some just won't tell you the bad news directly and they may foot-drag and hope you go away or they may make silly excuses about being busy or whatever.  That's spineless and it's not right, but that doesn't mean it doesn't happen.

So, if you ask someone for an LOR and they don't seem to want to do it, you should probably just ask someone else.