Odd plumbing issues

The master bath toilet has been making gurgling noises for several minutes the last few days now after showers are taken–air in the line?–but no other signs of distress. Until this morning when the shower in that bath did not completely drain after TS1’s morning fresher. Drano cleared it but when I ran hot water to flush, the water once again did not drain. Indeed, some water backed up into the tub in the other bathroom and that room’s toilet didn’t properly clear when flushed. A second application of Drano let the water go down again and this time no water left standing. Still, I think I want to snake the line after the stores open so I can get one.