を押して / を押し切って【をおして / をおしきって】

を押して and を押し切って mean going ahead in spite of an obstacle, named by the noun straight in front. を押して pushes through a condition, usually your own – illness, injury, bad weather – and を押し切って overrides other people's resistance.

を押して or を押し切って

を押して is about bearing a hardship: you go on while it is still there. Its nouns are a fever, an injury, pain, むり無理 (overdoing it), the weather.

を押し切って is about winning against someone: an objection, a refusal, someone trying to stop you. Its noun is almost always はんたい反対 or せいし制止, and the people come before it with の.

はんたい反対をおして押して also occurs, but it means going ahead with the objection still standing; を押し切って says you overrode it. Illness and weather cannot be overridden, so they never take を押し切って: ×病気を押し切って.

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Both belong to written Japanese and news reports. In conversation you would say 〜～のに or 〜～けど: ねつ熱があったけど、しあい試合にでた出た, おや親にはんたい反対されたけど、けっこん結婚した.