There are two theories of character. One, to which most people give lip service (at least) today, is the one that Galastel has expressed: characters, like people, are complex multidimensional constructs. This view of character seems to come from the modernist school of literary realism. It can, according to what I have read, but have not independently verified, be attributed to EM Forster.
The other, of which the critic James Wood may be the great contemporary expositor, holds that great characters are simpler than that. Rather than having all the shades and ambiguities of actual people, they are far simpler, exposing a single human trait. Their complexity comes not from the juxtaposition of multiple traits, but the thorough exposition of just one.
Some of the greatest characters in literature fit this model. Uriah Heap, for instance, or Quillip, or Little Nell, or Scrooge, or... well... any Dickens character you care to name. Captain Ahab. Gandalf. Lucy Pevensie. Emma Bovary. Becky Sharp. Jean Brodie. Jack Aubrey. Kurtz. Pinkey (either one). Hulk Hogan. Mr. Toad.
I am of the latter school. A story is neither a window nor a mirror but a lens. It brings one aspect of human life into sharp focus. It produce a sharper, clearer, simpler, more digestible, more exciting, more colorful, and more satisfying kind of experience than ordinary life provides, which is why we value stories in the first place, since the the experience of the murky realities of actual experience are available to us 24/7 if we want them.
And so a character is not as complex as a real person. Real people seldom act because their lives are too complicated and their spirits too weak and oppressed. They yearn for the shining stars of bold action, but almost never act like them. We want characters that are bolder, simpler, more vivid than ourselves; characters that are easy to grasp, to anticipate, to cheer for or to hate; characters, above all, who get on with things in a way normal people almost never do. Characters are not round, they are pointy.
So yes, two sources of conflict may indeed be too many. One source of conflict is plenty to drive a great story. And managing one convincingly, while maintaining tension throughout the story, and bringing it to a satisfactory climax and conclusion is difficult enough. Trying to do it with two may well prove impossible.
Don't confuse this, though, with having two sources of opposition. Characters with one problem often have multiple sources of opposition, because it takes multiple sources of opposition to force them into a situation where they have to finally confront their problem. No one wants to confront their problem. It wouldn't be much of a problem if they did. They have to be forced by circumstance into having to confront it. Trying to do that twice in one book is a tall order, and it simply is not necessary to create a fine compelling story.
My advice, therefore: pick one.