CELTA is an accredited body of educators - this means that they are real people (check out
CELTA - Certificate in English Language Teaching to Adults). This is going to be a rather expensive course and it's usually directed toward people whose first language is English. TESOL is merely an acronym for "Teaching English to Speakers of Other Languages", much like TESL or TEFL. There's not much difference between them. "TESOL" is not a internationally accredited body. It's just a field of study and work. You can be a TESOL teacher who studied at CELTA, but you can't be a CELTA teacher who studied at TESOL.
As far as what you think is the best for you, I would not be so presumptuous as to try to give you an honest answer to this question. There are so many variables involved that it would be impossible to assess without at least a 30 minute interview and overall evaluation.
Now, having said that, I would imagine that your best bet would be to carefully research different TEFL / TESL / TESOL school and ask around carefully to find the right one for you. Try to find out if that school even accepts speakers of English as a second language. Some don't even want to be bothered.
Good luck to you.
Don