Yeah... definitely more a technique issue. The recording process is far less forgiving than practicing/gigging. Every little flaw comes out. The good news is it will make you a better player. Keep practicing into the DAW paying attention to every movement you make. Warming up with some scales and position changing exercises beforehand is advisable. Also some guitars can make the little imperfections stand out more so if you have other axes around give them a try or rent/borrow something. A lot of dudes will keep guitars around specifically for recording (I bought my Yammie because I didn't trust my other guitars although they were good live).
As far as effects someone mentioned R-Mix. It is really good for doing precise surgery on stuff like this. Just watch the R-Mix window when you hear those squeaks and squawks then isolate where the little blobs show up when it's happening. You don't even have to turn that area down all the way. Just enough to keep it from overpowering the rest of the signal. Also if you are using a sim like TH2 or GR make use of the global gate features. May not do much in the middle of a performance but it can help tame things a little. Compression can help smooth things out a bit better too.
Just some extra things for you to try. Obviously checking out different options to see what works for you is best.
Cheers.