Lots of good advice, but a couple of points I disagree with.
Most soldering iron tips should NEVER be filed or treated with anything abrasive. The reason is that the tip is a copper core with an iron coating. The copper is for good thermal conductivity, and the iron is to protect the copper from the solder. You see, copper dissolves in molten solder. If you remove the iron coating, or even puncture it, the copper will rapidly disappear!
If you are having trouble getting a good joint, it's probably because you can't get enough heat into the star, which is designed to suck heat away as rapidly as possible. You want as much of the tip in contact with the pad as possible. It's best to contact both the pad and the wire at the same time, with a tinned tip, to get the best heat transfer. Putting the tip on top of the wire will make it harder to heat the pad sufficiently.
And to address the OP's original question, yes and no. You shouldn't reinforce the finished solder joint, you should secure the wire near, but not on the joint. It's actually best if you do it before making the solder joint, to ensure there's no residual stress in the joint. And use something more rigid than silicone. At work we use Locktite 444 cyanoacrylate on small wires (usually 20-30 ga.) and a special epoxy on larger things. We also use a urethane adhesive that remains flexible, but much harder than any silicone I've seen. It's similar to AquaSeal or Goop. Unfortunately it takes hours to dry, and I can't remember what it's called.
I'd recommend you go to the local hardware store and ask for a thixotropic epoxy (one that won't run). You might try epoxy putty, but I'd guess it won't be sticky enough.