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If I feel I'm lacking some kind of skills and I'm desperate to learn something, can I say "I need to recharge myself"?

"Recharge myself" is a good phrase, but it has the wrong meaning.

"Recharge my batteries" is perhaps more common than "Recharge myself."

The Oxford dictionary gives "recharge" with no object, -i.e. "I need to recharge," not "I need to recharge myself", as well as "recharge my batteries."

However, the meaning is "I am mentally or physically exhausted and need to take some time out to recover," not "I am lacking some skills and need to learn them."

Recharge myself is not a phrase I've ever encountered, but it's a nifty metaphor. However, I would take it to mean "do things to get myself more motivated and energetic":

I need to take a vacation to recharge myself.

When we speak of fundamental training or re-training to acquire new skills or roles the current catchphrase is re-invent myself:

I need to re-invent myself as a teacher.

And if the skills you do have are not as relevant now as they once were, there is the phrase to retool, that is, to acquire a different set of skills than the ones you have now.

She knows all there is to know about Microsoft Windows but because the market is shifting away from desktop applications to mobile apps, she really needs to retool.

P.S. This manufacturing term has been "co-opted" for general use in AmE. It is used figuratively in a wide variety of contexts from golf swings to school course offerings to football team rosters to the set of legal skills a law firm has to offer to software and tech skills, as in my example.

As other answers have pointed out, "recharge myself" IS a phrase, but it means something else.

To say what you are asking for (in a way that sounds like the phrase you used), that you want to gain skills that you are lacking, you may want the phrase "refresh my skills" or that you "need a refresher." That implies that you already KNOW the skills, and you just need to relearn them, or expand on them.

To learn NEW skills, especially if you are "desperate" like you said, you could say that you need a "crash course." Which would be a quick way to learn skills, albeit more of an overview of them.

It's a phrase not very likely to be said by a native speaker. It sounds like a direct translation of a non english analogy.

I need to rest, to have a rest, take a break, get my energy back, to chill out, are far mor common. Charge is from latin and is mostly the same in all latin languages, it vaguely means to load.

If you are lacking in skills and you need to learn something, you would say: I need to learn, to study, to do a crash course, to refresh my knowledge on.

"I've got to recharge myself" = "I've got to go recharge myself" = "I've got to recharge" = "I've got to recharge my batteries"...
Meaning: Eat, sleep rest; as in rejuvenating oneself.

 Being desperate to learn something is quite different than that; though resting is part of the process of learning. "Recharging oneself", could be physical and/or mental.
 If you wanted to express "desperation" to learn; it's ok, but not the best. Many people equate "desperation" with weakness; though not so much when your expressing a desire to learn. A more positive way to express this may be to say, "I am very interested in learning more about...".

I'm desperate to learn something, can I say "I need to recharge myself"?

You charge a battery with what it's supposed to be charged with (chemical energy), not something new. That's because the prefix re- means "again".

https://www.dictionary.com/browse/re-

a prefix, occurring originally in loanwords from Latin, used with the meaning “again” or “again and again” to indicate repetition, or with the meaning “back” or “backward” to indicate withdrawal or backward motion:

Thus, as mentioned in an earlier answer, you recharge yourself with something that you need again: enthusiasm, determination, love, etc.

@StoneyB's answer of using "reinvent" is correct in that when you learn something new to change the course of your life, you are "inventing (creating) yourself again" (since you invented your current self at a younger age).