New to Interval Training

Okay so I recently got a new gym membership and I wanted to try something new.

I used to do 45-60 mins of moderate effort on the elliptical (I get shin splints on the treadmill) and never got really good results. I would do this on and off at different gyms over the years as I moved around. I also played games like Just Dance for cardio.

I've been researching a lot about interval training, and tried it for the first time yesterday on the elliptical. I wanted to puke and had a coughing fit during my 5/6 rep but got through it all, with the last rep being okay. I warm up for 10 minutes on the elliptical getting my heart rate to about 165, then I do 30 secs sprint upping the resistance to level 7, and then lowering it back down to level 1 for 90 secs. I do this six times and cool down for five minutes. Since I'm a beginner I plan to stick with this for a couple of weeks and then tweak the sprint and recovery session. When I sprint, my heart rate jumps from 165 to 185, and when I rest it goes down to 170.

My height is 5'6" and my last weight-in at the doctor's was 180lbs. A couple of weeks ago.
My resting heart rate is 85bpm.
I have high blood pressure, cholesterol, triglycerides, and diabetes. Pressure and glucose are controlled; need to lower the lipids.
My muscle mass is 56%.

So how is my heart rate? Is it normal for this workout?

Also, I read that one should only do interval training 2-3 times per week. It takes me about 20 minutes. What should I do after, weights? And in what manner?

Say I do interval on the elliptical on Monday. Afterwards I do weights? My next interval training would be on Wednesday, but should I do to the gym on Tuesday? If so, what should I do?

Looking forward to your responses! I tried looking for answers but couldn't find them. Thanks so much!