You are trying to do too much.
I started running in January; I've been cycling for 9 years and been involved with various other aerobic activities at the gym for 25 years. I find that if I want to continue cycling the same number days a week, at the same intensity, I can't run more than 2 days a week. The few times I have run 3 times a week, I can't ride as much as usual. Granted, I am 55 years old, but since cycling is my first "love," I am not going to do anything to ruin that. I really like running, but there's a lot more injury potential.
It sounds like you are trying to keep up with your BF, who is at a different level than you are. You shouldn't end up crying on a ride! Either work out a way to ride together that you are comfortable with, or find others to ride with. Riding should be fun. You can train and improve your speed, but right now, what you are doing will lead to nothing but frustration and maybe injury.
And active rest means a walk, easy yoga, or stretching.