Deadlifts & Lunges causing problems!

So I have been religiously doing heavy weight lifting since January. I started on machines and then about a month ago I started transitioning to compound moves using mostly free weights. I started with squats with just a 45 lb. bar. So far so good. Then I added more weight to get to 60 lbs. Still fine. Then my trainer added alternating lunges to my routine after the squats. I pulled my right gluteal and had to take the week off. Grrrr. Then I resumed squatting and he had me add the leg press machine and avoid lunges for that week. Fine. Then the following week he had me do squats, deadlifts for the first time and walking lunges. When i got to the walking lunges, my legs were so toasted at that point, that I had a hard time doing the lunges on the right leg (it kept going to failure each time) but I finished. Today I did my legs and I did deadlifts first (60 lbs) and when I went to do squats, after my warmup set, I could feel my left gluteal hurting. I decided to back off squats and went to test out lunges. Sure enough, I could not do lunges or else I was going to blow out my gluteal even more.

I have been taking spinning classes (including yesterday) and wonder if that might be contributing to the sensitivity?

I am frustrated! Am I doing too many leg moves per session? I don't want to keep getting injured and I want to be able to progress in my lifting/fitness.

I am stretching religiously after all workouts and use the foam roller, too.

Any advice or similar experiences?