I just created a database/opening tree, populated with nearly 5,000 Evan's Gambit games pulled from the 2010 MegaBase. Don't know why I haven't built one of these before, lol. I'm running your game through it now to look for likely improvements during the opening phase.
In the 5. ... Bc5 variation, it looks like 7. 0-0 might be a stronger try than 7. cxd4, as you played. Castling shows up 344 times in my database, for a 72.4% score, average rating 1875 for those who played it, and average performance rating of 1889 (+14 points). Your cxd4 try shows up 200 times, scores 66.8%, average rating 1599, performance 1565 (-34 points).
Edit: Now that I have some more time, I'll come back and add a little about why this moves is better, instead of just quoting database stats. The point of castling first is to avoid Bb4+, after which it's a little tough to avoid liquidations of material that leave white without enough compensation for the pawn. After 7. 0-0 d3 8. cxd4 Bb6 white has a nice development edge and plenty of attacking chances. And 7. ... dxc3 8. Bxf3+ is even better for white.
After 7. cxd4 Bb4+ as played, you have the option of blocking with Nd2 instead of Bd2. Bd2 is the more popular move, scoring 62.4% in 109 tries (Avg 1525, Perf 1436). The less obvious Nd2, though, scores 85.3% in 39 tries (Avg 1818, Perf 1998). That's starting to get pretty thin on the sample size, but the stats are so much better that I'd definitely give them some credence still. And while engines are kind of silly to use for openings, I'll add that at depth 20 Houdini does prefer Nd2 as well (+0.04, compared to =0.00 for Bd2). The engine analysis doesn't mean much, especially with such a razor thin evaluation difference, but since I happen to have the info at my fingertips I figure I might as well share it
After your opponent played 8. ... Qe7 the database no longer means much as it cuts our sample size down to only 8 games (Bxd2+ is the standard move there, played 93 times). You were still within the database through 11. Qb3, though, before your opponent deviated for good with 11. ... Rb8?? which Houdini says was tactically losing, until you gave the advantage away with 13. exd5?? which Do It Right already covered. If you want computer analysis you can get it yourself though, so that's all I'll say about that. From here, I'll leave it to others to analyze your middle game better than I ever could. Do It Right had a lot of good insights, imo.