Can dm, copd, htn or its medications cause rise in sgot and sgpt level?

Yes: Some medications for dm are metabolized in the liver. Most inhaled meds for COPD can also affect liver function. Some diseases of the lung, like Alpha one antitrypsin disease present as both COPD and liver enzyme elevation.

Not really: It is unlikely any of these diseases have affected your liver enzymes. Diabetes could cause a fatty liver which might do it but it is uncommon to see high levels of these enzymes. More likely the medications to treat your diabetes or HTN may be doing it.