Instead of just calling the extra $0.30, maybe consider making it $1.25 or $1.50 there. Try to judge what raise size will make it feasible for your opponent to come over the top, or at least that will create a big enough pot for you to shove into on the end. As it is, there will only be $1.50 in the pot going into the river, with each player still having $3+ behind.
The only play that compares to the call on the turn is the check-call on the end. I'd say this was about equally bad. The board poses only three threats to your set: unlikely AA and KK, and a really bizarrely played 45. This is the kind of river sets would dream about if they were sentient. What was your reasoning behind closing the action there?
Honestly? I'd made some bad decisions before this hand, which led me to doubt myself and put on the brakes. Normally, I always go at least half-pot for any bets on the turn or later, but something made me hesitate here. "Did I miss something again? Am I playing against a monster hand? Am I digging my own grave again? Why is he raising? Etc.
Feelings getting the better of facts.
On the river, I was surprised to get raised, as I didn't estimate his hand to be strong enough to fire back, so I was a bit taken aback when it happened and frantically started looking if I'd missed anything. Hindsight is 20/20, but I noticed while writing it out it didn't feel particularly good to write the turn and/or river posts.
For the record: I'm well aware I play far from great, but that's kind of why I post these hands and why I started logging my poker adventures
I'm absorbing all feedback and going to try and see what works and what doesn't next time I play