With relevance to physiotherapy and the importance of muscle anatomy & physiology therein, all I would be inclined to clarify in your mind is to know that in the lungs, deoxyhaemoglobin releases the H+ ions [formed by the reaction below] as these are displaced from the Hb by the binding of O2 to Hb.
H2O + CO2 ------> H+ + HCO3-
Oc H+ ions tend to reduce pH [cos H+ ions are what make an acid acidic], but remember that carbonic acid [H2CO3] is a weak acid, so the conc-n of H+ is not unduly high. Nevertheless, it is true that release of H+ ions [which will be followed by HCO3- ions due to electrostatic forces] from the erythrocyte will help control pH within the red cell.
The Bohr effect [shifting of the oxygen dissociation curve to the right in the presence of high levels of CO2 [hence of low pH] or of chloride] reduces the affinity of Hb for O2 so that in this situation [importantly in the metabolizing tissues including muscle], more oxygen is released to allow cells to respire [I mean the chemical process of respiration, not breathing, which is strictly speaking, called "ventilation"]. The Bohr shift also facilitates binding of H+ and CO2 to Hb, thus aiding its removal from tissues.
As to rupture of erythrocytes due to influx of water by osmosis, I have not come across any clinical situation where that occurs [there are several other causes of haemolysis], so I would say it is only theoretically possible, and would advise you to ignore this point to avoid confusion.
One final point to mention: please learn about myoglobin [present in muscle] and its differences from haemoglobin in terms of affinity for oxygen, since that is directly relevant to your profession.