Hi, Syagrius. I'm not sure how much this will help but here goes. First, I have had blepharitis and also been treated with Tobradex. Or, should I say I HAVE blepharitis -- that's the thing I most want to share. According to my eye doctor, it's a chronic condition. That said, the first time (and I think maybe the ONLY time) I was ever treated for it was when I felt something wrong, besides the fact that the place where my lashes met the lid was red and a little swollen. You can check on this with your own doctor but what I'm trying to tell you is that if this is the case, think of what you have as a flare-up and it WILL go away. Your lids might be a little red and if you look at the margin (where the lid and lashes meet) you might see a VERY thin white line, only visible to you, not to anyone else, even when the flare-up subsides.
Since I know I have it (or am prone to it), I make sure to pay attention to that area. I'm not sure we're allowed to mention names of products but as a female, I've abandoned the use of commercial eye make-up removers in favor of a thing that comes in individual packets with the word "scrub" in it. Never fear, you do NOT scrub the sensitive area, rather, you use it gently. Even though you're not female, if your doctor confirms this is chronic, you should use this at least a few times a week. Funny thing is, my mother told me that in the "old" days, she used to clean her margins with baby shampoo and a Q-tip. (And that's probably still just as good!)
Anyway, this was/is my situation and I hope it helps. One (maybe two) flare-ups in the past 10 years and it's not visible to anyone but me!
If you feel that the medication is not working for you (can't remember the time frame for recovery) you should call your doctor and give them an update though.