How to analyze across three groups?

#1
I am working on a analyse of the effect on drugs for physiologic variables. It is retrospective, no randomisation.

My explanatory variables is
* Drug (3 groups: no drug, drug A, drug B)
* Age (continuous)
* Gender (male/female)
* Disease (7 groups)
* etc...

Measured variables
* Respiratory rate (RR). Five-level ordinal categories. Measured before (RR1) and after (RR2) drug is given.
* Difference in Blood pressure (BP). five-level ordinal categories. Measured before (BP1) and after (BP2) drug is given.
* A weighted scoring variable for physiology (continous) is calculated based on these values before (Score1) and after (Score2) drug is given.

Result variables is
* Difference in Physiologic Scoring (continous) - Score2 - Score1
* Difference in Respiratory rate (RR2-RR1).
* Difference in Blood pressure (BP2-BP1)

So, now I am wondering how to proceed...? Maybe
* Triple comparison- compare 1) drug A vs no 2) drug B vs no and 3) drug A vs drug B
* Linear regression?
* Factor analysis?
* Generalized linear model?

Any suggestions? Recommendations?

Best regards
Ole