No. Not quite right. I hope you've recently taken a full backup. If so, then you can take your log file backup and then immediately do a shrink if you need to for rapid recovery for DR purposes. If it doesn't shrink, take another log file backup followed by a shrink.
Only go to SIMPLE Recovery if you need the log file to shrink and it won't. Since you've taken a recent full backup, you only need to take a DIF backup followed by a log file backup both after returning to the full recovery model.
You also need to figure out why your log file was full. Is it because you're not backing up the log file on a regular basis or too long a basis? Easy fixes for those. If it was something else, you really need to figure out what it was and fix it. Another consideration... Could it be that the log file is simply too small?