Is 1/21 an actual trial date, or a trial setting conference date? Have you exchanged witness lists, exhibits, exhibit lists. stipulated facts, jury instructions and statement of the case (if you have a jury), etc.? have you subpoenaed your witnesses? Your case's motion cutoff date should be long gone, and the only motions that are heard at this point are motions in limine. Your statement that "they are theatening new charges" is confusing, since complaints can't be amended this close to trial, since you'd need to be able to file an answer and both sides would need to do discovery.
Since you state that your lawyer is getting out, that sounds like you don't have a trial date in 5 days, because your lawyer couldn't get a motion to withdraw granted so close to trial, although you could let them out by signing a Substitution of attorney form. Also, trials don't usually start on Thursdays, unless it's a one or two day bench trial.
You can check with the court clerk to see what the likelihood is of actually starting on your set date. Judges try cases consecutively, and it's a scheduling challenge because some cases settle, and the next case in line has to be ready to go so the judge (and any empaneled juries) don't have down time.
Get a lawyer, or keep the one you've got, if you can. It's really not smart to try to try your own case, you're probably your case's main witness, also, and it will be awkward, not to mention the fact that you don't know the procedures.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Superlative response by the other counselor. The only thing I might add is that 1/21 is in all likelihood a trial readiness conference, or perhaps even a mandatory settlement conference. I reiterate that no new "charges" are possible so close to trial. I might suggest that you seek other counsel if your present counsel's motion is granted. If such occurs, a continuance will inevitably be granted.
Look I don't recommend you represent yourself. There are too many traps for the unwary. Get a new lawyer immediately so that the judge does not believe that you are trying to stall. If you cannot afford a lawyer you should ask for new appointed counsel asap. I do not know anything about your case but it is usually to the defendant's advantage to start trial sooner rather than later.
Just so there is no confusion, I feel compelled to correct a few things that my colleage Ms Koslyn stated in her answer.
First, a 0 of 10 date is a "Readiness Date" where the court will expect both parties to announce ready or have good cause to continue. Second, if both parties announce ready or are deemed by the court to lack good cause for a continuance the case can be started that day or any day within the next 10 days. Third, criminal courts in LA start trials every single day of the work week. Fourth, the in-custody 10/10 trial matters will be given priority. So if there are too many cases in front of you (very likely) and not enough courts to hear your case, it will be trailed to 8/10, 9/10 or 10/10.
Fifth, in criminal cases, the information (felony cases) or complaint (misdemeanor cases) can be amended at the last minute with leave of the court, but, in the case of a felony, only if evidence of that crime was presented at the preliminary hearing. (That is, if you know enough to know what to object to and how to make your record -- prime example of why you should not represent yourself.) Also, let's say this is a misdemeanor case or that there was evidence of this previously uncharged crime offered at the PH, if the defense can show how they will be prejudiced by the late amendment, the court will either have to deny the additional charges or give you time to prepare for those new charges. Again, if you don't know how to show legal prejudice and why you are unable to defend on those charges, you will not be able to establish good cause for a continuance.