I'll start by saying that without examining you or knowing the particulars of your surgery the following is general rather than personal or specific advice.
Failure to create an acceptable flap is a known albeit rare problem which can arise during a LASIK procedure. There are multiple reasons why this can happen. Perhaps your surgeon can explain why this occurred in your particular case. If a suitable flap is not made, the vision correcting part of the LASIK procedure cannot be performed.
It sounds like your surgeon took the proper action and put the LASIK flap carefully back into place (without trying to correct your eyeglass prescription). If you can see pretty normally with your glasses it means that things are going extremely well.
While frustrating, no attempt at a new LASIK flap should be made for at least a few months. Trying to proceed sooner could create "intersecting" flaps, flap fragments and all sorts of big messes.
Some surgeons prefer to change plans from LASIK to PRK (LASIK without a flap) when this type of issue occurs.
Have you had a chance to sit down with your surgeon and have all of your questions answered? I am sure, especially in this type of disappointing circumstance that your surgeon wants to have especially good communication with you. Be assertive, tell all the support people that you want to talk directly to your surgeon about what happened.
LASIK starts out with such high expectations which are met the vast majority of the time. When situations like this arise, disappointment is understandable and poor communication makes it worse. Both you and your doctor need to form the best kind of professional relationship because you are going to get to know each other well during the coming months.
This type of "complication" can be fixed and often times with a result every bit as good as if it never happened. However, patience is a virtue.